I'd look for a booking in Broome asap. I was chatting to a rellie who spends a month in Broome each year and has a regular booking. He said they're very fully booked.
I know when we went there years ago we had to line up outside a caravan park and wait till someone left.
It's a great place to visit but not if you have difficulty getting a spot.
It may have improved and they may created some overflow accommodation but I'd be careful.
We stayed in Broome last year, peak season, and stayed at the SDA(Seventh Day Adventist) overflow park on advice from a fellow traveller in Alice Springs.
For us it was worth it @ $35 p/n for a powered site for family of 4. The sites were cozy, but that didn't bother us as we were out most of the time anyway. They have a maximum of 7 nights as well.
No playground or swimming pool, facilities were basic but neat, clean and well maintained. We had to call each day to see if there was availability as they cannot take bookings. We were catching up with friends so it didn't bother us waiting a couple of days.
They say to book ahead, but on coming back from Cape Leveque, we managed to get a powered site at Cable Beach caravan park for the same day after trying a couple of other places.