A royal convoy with a leisurely pace and a fat, comfortable king would not reach near as much, though ^^
Adds that even with roads, terrain is not flat, and that a road doesn't go in straitgh line so if it's 2000 miles on the map, it's probably closer to 2500 or 3000 on the ground.
So count maybe 10 to 15 miles a day, for 2500 to 3000 miles... It's closer to one year than one month![]()
Which brings up back to how poor an idea it was for known Westeros to be the size of South America

And really Martin had no reason to do it, even if Westeros should 100% be its own continent. Since no one knows what is north of the Wall anyway, what is south could just be Britain-sized with not as much issue. The different weather/climate is an added problem there, but then again that isn't that needed an idea in this scale either (why should Dorne be a desert at all? It could just be a lot warmer than in the Wall, but still continental-like, and i am sure they will model it on the euro med anyway in the show).