I think you are supposed to go ahead and do it as soon as you have all the info available. That was it's already processed and accessible to the school when they start handing out aid. There's really no reason to wait anyway.
Besides, if there are need based scholarships, the funds may be limited. Some aid may be first come, first serve.
Fill out your FAFSA as soon as possible and get the basic info all put in there (demographic info, tax info, get a pin number, etc). You can always just put down your top choice school for now. It's very simple to just add/remove schools later, and do that as soon as you know for sure which one you will be attending (click "make corrections to a submitted FAFSA").