We always go in the summer, but stay at the Marriott timeshare next door. As far as I can tell, they're always pretty high occupancy. I would guess it's the same at Aulani - you won't likely find any time of the year where the occupancy is very low! It's a popular resort for families (both are really)!
I'd start looking into airfare now. We typically have ours booked anywhere from 8 - 10 months out (we always use miles to pay for us). Not sure where you're flying from, but it pays to check multiple airports if you live near more than one. We usually fly out of BWI, but have used Regan National and Dulles (once, yuck it's further). For one flight from DC, the kids and I stayed the night before across the street at a hotel, since we had to be at the airport at 5am - you can't count on traffic even at 4am around DC!