I moved while 3 months pregnant with my second and I'll be moving again while 4 months pregnant with my third. While it's certainly not ideal, it's totally possible to find good care after moving. In fact, after moving here while pregnant with #2 I hired the first midwife I interviewed and ended up letting her go when I was 36 weeks and hiring a different one. Switching midwives that late in my pregnancy worked out just fine. We clicked with the second mw immediately and felt quite at ease with her. So even if you don't have your entire pregnancy to form a relationship, you absolutely can connect with your care giver and have a great experience. There are all sorts of ways to research birth options ahead of time, before you move, so you can get right to work interviewing as soon as you arrive. I tend to look for natural parenting or attachment parenting Yahoo groups, which I join before moving and ask all sorts of questions.
All this being said, though, moving to a new area when pregnant is NOT fun. It's not fun to pack and unpack while nauseous or fatigued. It's not fun to drive/travel to the new place while nauseous, fatigued, and in your case possibly feeling bigger or having pains from sitting in the car (at 7 months). It's also not fun to have to find your way in a new city, make new friends/neighbors, look for new playgroups, etc. while pregnant. It's hard being new and not having anyone to bring you food after the baby comes or to help hold the baby while you shower. It's hard not knowing where any of the parenting stuff is and having to figure it all out in a new place. It's hard feeling unsettled and uncertain.
So, quite frankly, if I could avoid it, I would absolutely not want to move while pregnant. But not knowing what else is going into your decision for timing this pregnancy, it's hard to advise. Plus, if this is your first pregnancy, there's no guarantee that you'll conceive as soon as you start TTC. You might get pregnant right away or it could take several months and then you might be moving while in your first trimester and dealing with morning sickness. Is it possible to wait until after you move to TTC?