It depends on what culture(s) survive the apocalypse
The size and composition of a country's military has far more to do with cultural values and socioeconomic factors than it does with its actual size. While creating and maintaining a single world order can be done in many different ways, it is important to note that no land mass anywhere near as large as the Earth could possibly have a single distinct culture.
Infact, most large nations today can be broken up into a number of different cultural zones which can make creating and keeping a unified identity in this one world order extraordinarily hard. This means that you will first have to resolve how your government will get your hundreds of global subcultures who all want different things out of thier governments to cooperate... which is really to say what culture will come out on top to impose its ways on everyone else.
While the common enemy aspect of the Dawn Wars time period might make a global alliance possible, cementing it into an effective singular world government in the aftermath will not be easy. So, what happens to the military afterwords is going to be based on who takes control of the peacetime propaganda industry.
To try to solve this problem you should first decide what parts of the World were most/least decimated by the Dawn Wars. Those that escaped least harmed will be far better at imposing thier will on the rest of the world than those that lost everything and were forced more into hand-to-mouth life styles keeping them from becoming politically active in the aftermath.
Once you know who the big contenders are, you need to find out how these peoples view thier militaries. In some cultures, the military is seen as a safeguard against intangible threats, while in others it is a thing that should only be there to deal with tangible and persistent threats. Some cultures see a standing army as a symbol of strength and solidarity, while others see it as a symbol of oppression. Some see it as a rite of passage for young people while others see it as oppressive to young people.
Ultimately the continued strength of your peacetime forces will be the object of propaganda more than any actual and immediate need, but that propaganda will be vital to making sure that you appease the majority faction(s) or else the confederacy will fall apart and you will not have a one world order scenario for very long.
Understanding your Limits
At the high end you have North Korea which requires 5-8 Years of Compulsory Military Service for all of its able bodied citizens. This puts about 5% of thier total population in active military service and 2.3% of thier population in reserves for a total military strength of 7.3% of thier population, but this is a really bad for North Korea's economy because it takes thier entire young adult population out of education and the workforce significantly limiting thier opportunities for effective higher education and heavy labor occupations. North Korea can only justify this large of a military through a combination of very specific cultural values, and it's position between the much larger and economically powerful nations of China, Russia, and Japan. It is very unlikely that a world order spanning many different cultures would abide such a large military unless the propaganda is really good at upkeeping the perceived threat of a renewed Dawn War era.
Then at the low end, you have 3 reasons why a country might have a particularly small military (under 0.2%). First you have countries that are too small or improvised to justify a functional military. These countries won't really apply to a one world order scenario because they tend to be breeding grounds for cartels which would go against the one government idea. Then you have countries that are geographically isolated and in good enough political standing with thier neighbors to not see a need for a large military. Canada is a good example of this with only 0.18% the total population in the military. Third you have counties with too large of a population to need to commit a large % of people to military. India for example only dedicates 0.1% of its population to military despite having the second largest military in the world. So, they see 0.1% as enough to serve the need. It is likely that your world government will take an approach similar to India or Canada if your world government pushes the narrative that the world is safe, that the Dawn Wars are a thing of the past, and that the likelihood of future wars is negligible.
Then in the middle you have countries where military service represents a way to give opportunities to an otherwise struggling lower class. In places like the United States (0.4%), military service is still voluntary, but participation is notably higher. In countries like the USA, the propaganda is that joining the military is a good way to uplift your future. So, even if your world government does not see an immediate military threat, it could choose to maintain a significant military due to the economic and welfare opportunities created by the military industry and powerful special interest groups that profit from keeping it well maintained.
Lastly, you have the citizen soldier model. This idea is not very common in modern warfare because modern weapons and tactics require too much training, but if technology regressess enough after the fall, it could be possible for your country to revert to a large standing militia where 10% or more of your population has a legal obligation to arm themselves and respond a draft if called upon, even if there is no standing army.
