I am due in September. I requested a booking at Matilda at 7 weeks and was put on the waiting list. I called them and I was #1 on the list. Confirmed patients are given 4 weeks to pay the $20k deposit. At 16 weeks they confirmed a bed for me as others didn't pay. I'd say if you're # 12 after the deposit deadline your chances are slim. Beds might open up as people may have to deliver at QM due to complications, or some miscarry, but I think most people that pay the deposit will have their baby there as it is non-refundable unless there is a medical reason.
My suggestion would be to give Matilda a call and find out when the deposit deadline is for your due date. Once that's passed if you don't have a bed find out your number on the list and if you're not top arrange for an alternative. The midwives are great and will recommend that anyway if they see no chance for you.
Good luck!