Congratulations on the new job! Great question, too. Most of the discussion on this issue revolves around school aged children, and childcare for them during track out. There has not been the same public discussion about the possible increase in childcare costs for teachers. I used to teach in Wake county, and our family had the same discussion - I was offered a position at both a traditional school and a year round school, and the difference in childcare was a big piece of the decision for us. Surprisingly, the childcare issues for year-round actually are not as different as those of traditional teachers.
Typically, for a traditional teacher, the daycare center will allow you to pull your child out for the summer, but if there is a waiting list, or if the classroom fills up, you run the risk of losing your "spot" in the fall. Most centers will offer some kind of flexibility or courtesy to give you the option to either then pay for the summer if and when this happens, or allow you to reenroll, sometimes with a reduced re-registration fee.
The same thing happens for year-round, only instead of pulling your child out for ten weeks, you do so for three weeks at a time. Again, if there is a waiting list for the classroom, you have the option to continue to pay to reserve the spot, or not. Most centers, however, will not make you pay if there is no waiting list, and I know of at least one in Cary that allows you to pay 1/2 tuition to reserve the spot. As more schools go year-round, more child care centers are going to be facing this issue, and my experiene has been that if you talk to the owner or director, they will offer you some flexibility.
Also, while doing your research, find out if the center offers a discount for teachers - mine did, 15% at the time, which made a huge difference when working on a teacher's salary!
The thing is, I didn't know to ask until after we were enrolled, so it was a very nice surprise.
(btw - if you need advice on licensure and the hiring process, or more specifics about this topic, just drop me a pm!)