I changed doc after my 1st fresh and 1st FET.
From what I understand, FET have to be at least 3 months after a fresh cycle, so whether your change doc or not, you can proceed with your FET at your next menses after your 1st appt with the new doc or after the 3rd menses with your current doc, which ever is later.
With my previous doctor, he also did not scan bladder or scan while placing the embryos.
With Dr Tan, he will scan bladder and scan while placing embryos BUT you cannot see as the screen is facing him, unless your trf happened to be in OT (which happened to me once since it was a Sat afternoon).
I think whether or not to change it is your comfort level with your current doctor.
What triggered me to change doctor was that from the very 1st appt with the doc, I already felt uncomfortable as he was a guy with few words. Did not explain much and did not answer my questions clearly. I only proceeded with him as hubby felt that doc was ok and did not want to go through the hassle of changing and requeing. But after failing 2 cycles, I insisted on changing and I am comfortable with Dr Tan ever since.