Think a Lord of the Rings-esque quest to save their kingdom. This quest would also involve detours, but I can just factor those in later. The continent is around the size of Australia, with a lot of grassland and a dense jungle in the middle. There's also a relatively large mountain range they have to cross, but they have paths to follow to make it easier going.
Let's do some basic math;
Australia is approximately 4000km wide, and a good figure for an average walking speed is 5km/h, meaning that in total it would take around 800 hrs to walk from one side of a continent like Australia to the other.
It's never as simple as that. For a start, it's not a perfect plain, food and water is not going to be distributed evenly across the continent, and inns aren't going to be in straight lines or evenly spaced. Also, you need to sleep, rest, etc.
So let's assume that we think of this trek as a job. That means, that we make 8hrs worth of progress each working day. Let's further assume that we only 'work' 6 days a week. This gives us some time to double back when we forget our favourite elven sword, go sideways to find food or a water source, and also account for the fact that sometimes the best inns to stay at are only 6hrs walk from the last one.
That means, that we're talking 48 hrs of progress per week, and that equates to 240 km. Let's round it up to 250 because our warriors are eager to pursue their quest and because it makes the math easier - It's going to take you 16 weeks, or nearly 4 months.
Of course, that's setting a more blistering pace than you might like. 8 hrs marching per day sounds wasteful, but remember your questors need to carry armaments and supplies, at least some water, potentially food reserves - unless they have carts and the like, that's actually quite heavy going, and even with carts that is going to wear them out pretty quickly. So, there are going to be stages where they need more rest, and this also doesn't factor in inclement weather and the like. If you factor in another 50% for fatigue and bad weather, let's call it around 6 months.
There's a lot you can do to alter this figure in your world of course; the basics are all in this explanation, the rougher you make it on your questors, the longer they'll take. If you give them horses and the like to carry their stuff, and support teams along the way, they may actually make it faster.
The one thing that's absolutely certain - don't try this in REAL Australia. The middle of our fair continent is essentially desert and many people have died out there in cars and the like because they didn't carry enough water and other essential supplies and have broken down. I mention this because if you put ANY desert or dangerous terrain between your starting point and your destination, you dramatically increase time, risk and supplies needed to reach your final point safely.
For comparison, Roman soldiers were expected to march 30 km (20 Roman miles) a day with 20 kg equipment. The march itself was expected to take 5 hours, for a mean speed while marching of 6 km/h (a fast walking speed). The rest of the time was spent foraging and setting up camp, camping, and striking camp.
20 kg is a lot of baggage to carry around. According to an article about hiking, fit hikers can hike 25 miles (40 km) a day with a typical backpack (including tent and sleeping bag) daily for 4 months. This probably does not include time for foraging.
The average walking distance on the Camino Frances trail is 21-26 km a day, but typical Camino wanderers are ordinary people, not trained travelers. 30% of Camino travelers manage more than this, with 13% managing 31 km or more.
About 30 km per day hence seems realistic, even in somewhat rugged terrain, if the travellers are reasonably fit and don't carry too much. The walking itself would take 5-6 hours, leaving the rest of the day for rest, foraging, and camping.
Australia is 4,000 km east to west, and this would hence take 133 days or 4 months. The mountain range may add a few weeks to this estimate.
In the 1830s-1860s, caravans of Conestoga wagons and livestock and children traveled the 2000 miles from Eastern Nebraska to Western Oregon in about 7 months. Includes traversing multiple mountain ranges.
That's roughly 15 miles a day across easy terrain, 5 miles a day across difficult terrain, with daily time for foraging, cooking, laundry, making and striking camp, caring for the sick, rounding up wayward livestock, etc.
A healthy person can sustainably hike ~5hrs per day, but they can not cover the same amount of distance per hour depending on terrain; so, the ratio of mountains, jungels, grasslands and roads will make a big difference for your travelers.
There are a lot of conflicting resources and formulas for estimating hiking times through various terrains; so, I'll try to aggregate info to make some rough estimates. First off, this is a long march so assume you have a lot of gear putting your base speed at 2mi/hr instead of the more ideal 3-4 mi/hr a person can hike during a day trip. Second, there will be places that travel is VERY slow going like when you have to stop to climb a cliff or ford a river, so there's some guess work that goes into averaging out rough terrain.
Flat paths & roads: 2 mi/hr -> 10mi/day Unbeaten grasslands and sloping/gravel paths: 1.5 mi/hr -> 7.5 mi/day Sparse forests, loose sand or gravel, steep paths: 1 mi/hr -> 5 mi/day Thicker Forests, wetlands, and rough hills: .75mi/hr -> 3.75mi/day Mountainous or swampy terrain : .5mi/hr -> 2.5 mi/day
Next, look at a map of your trek and figure out how much you need to travel for each terrain type drawing a line through the rough you expect to take. For example, if you're spending a lot of time in the wilderness like in the LotR, it might look like:
Flat paths & roads: 800 mi Unbeaten grasslands and sloping/gravel paths: 600 mi Sparse forests, loose sand or gravel, steep paths: 500 mi Thicker Forests, wetlands, and foot hills: 400 mi Mountainous or swampy terrain : 150 mi
Then divide each distance by speed and add the number up for total days.
(80 + 80 + 100 + 107 + 60) = 427 days.
Your exact results may vary a lot from this if your group decides to mostly travel by road, or travel lighter, or if you decide they are exceptionally fit, or needs to take a 300 mile trek through the underground twisting caverns of Moria, but either way, you'll want to use a method similar to this to approximate your travel time, because without accounting for terrain, there is not really such thing as an average hiking speed.
The key question is if they will be able to get food from inns or markets, at least every couple of days, or if they have to forage practically all the way.
The Lewis and Clark expedition had slightly more modern technology, but it should be a good example. They did about 8,000 miles in 28 months, including lengthy stops over the winters.
For comparison, the Chinese Communists' Long March was about 6000 km in 370 days over rough terrain (9000 km according to the official Chinese line). Although they had roads, still, with tens of thousands, that's difficult movement.
In 1846-1847, the Mormon Battalion marched from Iowa to San Diego, covering about 3000 km in 6 months. Again, that's with a baggage trains, wagons, some extraneous people, and making stops along the way.