Yes, but Nait, we don't have to be picky and make the world perfect.
This is for fun, not for a freaking science project. When you have this large an amount of people toying with a world, not everything is going to make sense. So what if it doesn't fit in with every single law that Earthly history has taught you? This isn't Earth.
It's also possible that magic may become a part of this world, but we won't get into that just yet.
Just because the rabbits (or whatever) breed like there's not tomorrow doesn't mean we can't give them a short lifespan or a small appetite. These things can be worked around to suit humanoid survival.
Have the Pacific islands been inhabited for tens of thousands of years? =o
As for background of the other races... I don't see why you guys can't come up with that yourselves if you really want to.
EDIT: I'll say it again, though, if the only problem you have concerns the amount of time they took to get to the medieval stages, I'm happy to adjust that. I just don't want to change how they got there, or where they are at the point that we'll begin focusing on.