How early should I apply to housing?

UF is my top school, but my parents dont want me to go. Even though we are in-state and get in-state tuition, they want me to go to a worse, more expensive private school (10x the price) closer to home, which I dont want to do. Until we get this figured out, I can't even accept my offer, so I was wondering if there will even be housing in a week or two. Can I even expect to get housing atp