I moved a week ago and had only 2 weeks to find an apartment to rent out before we had to move out. Like many others I went on gohome, squarefoot, spacious etc. etc. to desperately try to find an apartment within our budget and that was fairly big. I did manage to find an apartment doing this, but I think I was really lucky to get a hold of an agent that still had the apartment not rented out.
BUT, it is so much better to go to the area that you're actually thinking of moving to and search for real estate agents there. There are some more local agents where they have quite good listings that the big ones like MIDLAND don't have. And if you actually visit the agents, they'll show you the available ones there and then and you won't have to constantly wait for them to call you back so they can "check if its still available"