I can't say for sure as its recommended to book it in advance but when we went last sept I booked it about 2 weeks before we flew and when I was on holiday I phoned up and changed my dates and there was still quite a lot of availability like 3 days before. Like I say, can't guarantee but from what I've seen and experienced I reckon you'll be ok
1st trip: 1985 - Travel Inn. 13 further trips as a child.
Trips with Hubby:
2003 - June Homewood Suite I drive.
2007 - May Homewood suites I drive.
2009 - Sept Animal Kingdom Lodge
2011 - May/June Disneymoon trip! BWV & AKL.
2012 - Sept The 'anniversary trip' SSR.
2013 - October the bonus trip to POR