My son has not started pre-school yet (he too is starting in September), but if it was me, my gut feel would be to start her anyway. Even if you did move by Christmas she would have had a couple of months at the school and got used to a pre-school environment.
I would start looking at new pre-schools now though in the area to see what the waiting lists are like.
I understand your worry about settling in then having to move, but I'm sure she will be fine (and at that age they can make new friends again quickly)
DD is 2.5 and has a place at a local pre-school two mornings a week, starting in September.
However, we have just sold our house and have had an offer accepted on a house in the town we are moving to. Nothing much has happened yet re: conveyancing on either of the houses we are selling/buying.
I'm in a real dilemma as to whether to start DD at the pre-school where we currently live. I don't really want to go through the whole settling in process and have her become attached to the staff there only for us to be moving away (possibly by Christmas) and to start again at a different pre-school where we are moving to. (I haven't started looking at pre-schools in the new town yet, so it is possible she may have to go on a waiting list for a place.)
On the other hand I realise that buying/selling houses can be problematic and there is always a chance that something might go wrong which'll mean we are still living here in 6 months' (or more) time. If this is the case then I'd probably regret giving up her place at our local pre-school.