There's several issues which should be addressed before you can establish a new world order:
Laying the Foundation
As Cyrus suggested, I would propose that you set up a group of people to kick start the re-population process before you unleash the virus. This way they will already look to you as their leader, and share your goals and ideals.
For example, you could gather a few hundred (or thousand) like minded individuals to come live on a remote farm. You can arm and organize them in order to protect and operate your facility - labs, fields, processing plants, etc. (the infrastructure doesn't have to be major, just enough to keep your group alive and at a decent tech level).
As survivors trickle in your group can indoctrinate and integrate them into your ranks.
As more and more people arrive you can start taking over the abandoned structures of nearby towns, and slowly expand.
Your group will have to be powerful enough to hold on to what they have, as well as impose their views on other groups they encounter.
If, for example, you run into a surviving military unit which claims that you should subject yourself to their authority, you must be able to convince them to join you, or fight them off.
If you run into a group of citizens led by a political figure who is trying to hold true to the Constitution/old government structure that might not fit with your ideology and objectives. You have to be ready to convince these people to join you, or take them out so that your ideology will prevail.
What this ultimately means is that you need a very dedicated group of people to act as the core of your community. A group of people who will borderline worship you, look to you as their leader, and follow your orders no matter what. It's far more difficult to establish this in the post apocalypse world than if you lay the foundations before hand (establish self sufficient facilities, recruit people to your cause, purchase arms, ammunition, seeds, provisions, etc.)
State of the World
A lot more technology will have been lost than what you're assuming (unless, of course, you also took major steps to preserve it). Keep in mind that you've killed off almost 7 billion human beings.
The world you'll be inhabiting is one forever changed. In the US alone you'll have 300 million bodies littering the landscape. This will cause pests, predators, and disease to run rampant. Animals which before were no threat to man will now multiply and get used to feasting on human flesh. This is a very dangerous setting for your followers.
Without human supervision a lot of infrastructure will have been destroyed as well. Power plants left untended will have suffered severe failures, fires, or elemental damage. Data routing centers will have similarly shut down due to loss of power, or other damage. This means that no, you won't simply be able to access the internet from any powered terminal.
Infrastructure will have been destroyed in humanity's fight against the zombies. Fires left unchecked will have burned down entire towns, and might still be raging in large cities more than several months after first being started, engulfing skyscrapers, and residential neighborhoods alike - the pollution would further harm survivors.
It won't be as easy as simply walking out of your bunker and claiming the world.
Loss of Technology
The sad fact is that the average human being is no smarter than people were 500 years ago. Sure, we're a little more educated, and have developed a different skill set than our farming ancestors, but it's still only that: a limited skill set.
What am I talking about and why is it important? People may know how to use a cellphone, or drive a car rather than plant and till a field, however very few of us understand the underlying principles or those technologies.
Good examples are cars, computers, and cell phones - something we take for granted on a daily basis.
Most of us know how to operate a motor vehicle, yet few of us have any idea how to perform more than minor maintenance, if that. If a car breaks down you need the help of an expert - a mechanic. The mechanic is, to us, a bit like what a blacksmith was to villages of old. He's an expert that can help you get your horse/cart/tool back in working order. However, while a mechanic may be able to take an engine apart and figure out what's wrong with it, he can't manufacture the complex parts needed to repair it. Specialized manufacturing capabilities and engineering knowledge is necessary for that. Experts in those fields don't grow on trees, and neither does the technology itself.
Computers are ubiquitous in our world. However, very few of us can take one apart and rebuild it. Even then, how many people truly understand how a motherboard, and RAM chip works? How many of us could build one from scratch? With what tools? You get my point. Cell phones are the exact same.
It was estimated, in a report I read a few years ago, that if you were to kill the top 10 000 or so technical experts in the world you would stop human technological advancement in its tracks, possibly for decades, and set civilization back, technologically. Why? Because only a very small number of experts truly understand the underlying principles behind a lot of these technologies. A lot of us might have some theoretical knowledge, or understand, in broad terms how a piece of technology operates, but only that handful of people would be able to sit down and design/build that piece of tech you take for granted.
And guess what. You've killed them all. This means that your group of survivors might scavenge technology from stores, warehouses, etc., but no human being will be advancing science again any time soon. You've successfully crippled the human race for generations.
In your title you claim that you want a more peaceful and equal society, however you're starting off my killing 7 billion people. That right there is a red flag.
Once society has completely crumpled you will step out into the battle scarred, corpse covered world, and find that chaos and violence rule the planet.
Groups of survivors will be living hand-to-mouth, scavenging the left overs from humanity's golden age. They will fight one another for the scraps of food, technology, ammunition, and fuel which they've collected. Bandit groups will roam the country - they will need to be dealt with, which undermines the idea of a peaceful society right off the bat.
Furthermore, in the absence of human beings predators will have bred and become far more confident. Wild animals will pose a pretty serious threat to people from now on. Your followers will need to defend themselves, which breeds a mindset of being ready to kill and be killed, not peace.
Last but not least, you've effectively plunged the world into a Dark Age. This is not a state of being which encourages equality between the sexes. Arguably, it's the industrial revolution which truly allowed women to emancipate themselves.
In a farming society which doesn't have the fuel or technology to sustain a modern farm women will ultimately revert to secondary roles. I'm not trying to be sexist, or misogynistic - it's simply the truth, however unpleasant. A woman cannot physically work the field the same way a man can, however your community will starve to death unless those fields are planted, tilled, and harvested.
This means that men will be required to perform the heavy lifting, while women will revert to the role of house wives: cooking meals for the men, raising the children, etc.
Some technological left-overs will allow them to perform other tasks. Modern firearms, for example, will allow a woman to just as effectively defend a fixed position as a man.
However it will become a lot more difficult to maintain equality when your society will slip back into classic gender roles (which are what allowed humanity to eventually reach this level of technological prowess - this was a "good thing" in the past, but simply not justifiable in our modern society).
Even if your community somehow manages to retain the mentality and technology which allow women the same rights, privileges, and opportunities as a man (due to your brilliant leadership, of course), that will certainly not be the case in most of the rest of the world. Women will have a tough going of it in this post-apocalyptic scenario.