Switching dr.'s two months before birth?

theatrelily

So, my husband is applying for a new job closer to home, and there is a very strong chance that he will get it.

 While I am excited at the prospect of the (much) higher salary and the close proximity to family, it would mean moving in June. 

Have any of you moved, necessitating a change in doctors and hospitals so far along in your pregnancy? How did it go?