I found that my DD was really adaptable at that age. Before we moved we mentioned that she might be going to a different school to the one we planned but didn't dwell on it and just mentioned it again once we actually moved. If you don't relay your (understandable) anxiety about school places to your little one then I'm sure they will take it in their stride.
It wasn't until we actually had the place that the did the whole uniform, getting excited about going to school etc. This was really hard because I really wanted to get excited about DD1 going to school, with it being a significant life event etc, and hated the uncertainty but it was a compromise we had to make for moving to a better house.
DD1 did have a momentary wobble (lasted about an hour!) about the school uniform colour and about going to a different school to her preschool friends but some new hairbands helped with the uniform colour and being told that her preschool friend were still her friends and she could catch up with them in the holidays and make new friends at school reassured her.
At this stage I would focus all your efforts on selling your house (if you are) and finding a new place to rent or buy and get all that paperwork in order asap so that you can apply for a place in your new area or get on the waiting lists of schools (depending on when you exchange contracts/ sign rental agreement etc makes the process slightly different). If it looks like everything is going ahead touch base with the Local Education Authority to check what the process is/what timings are.
Schools may tell you where you are on the waiting list but some are reluctant as you can move down as well as up if someone with higher priority comes onto the list (because they have moved in nearer, have a sibling that has transferred into school etc).
Be prepared to have to wait until term start in September before you get a school place as there is a lot of movement at the beginning of term.
As previous poster said you have until the term after their 5 birthday before they legally have to go to school so you may buy yourself some time that way depending when your child's birthday is, although this isn't ideal. I personally think it would be preferable to start at the same time if at all possible and wouldn't recommend waiting until after you child has started school before you apply for new places as it will be a lot less likely that you will get a place.