Voyager had nurses as well... They were all killedOn the subject of the EMH I doubt there would be any need for him at all if the E-E were in the DQ instead of the Voyager even if Beverley were to get killed. The reason being because the E-E has around 7 or 8 times more crew than the Voyager and would obviously have a more sizeable Medical staff with at least more than one Doctor. So if Crusher died then all Picard would have to do is promote the next Doctor or most senior Medical Person with the proper quialifications to CMO and that would be that.
So, it's possible that almost all, if not all, of Enterprises medical staff would be killed as well
The 1701D had Dr. Salar, and crusher mentions that it would be ridiculous for her to be the only doctor on board the 1701D in Remember Me. The full size of Crusher's medical staff is never revealed, but it should have been a good sized complement of doctors and nurses. It would be safe to conclude that the 1701E had more than one doctor. Even Kirk's 1701 had at least 2 doctors on staff.
Now Voyager left without a full crew (I seem to remember Janeway mentioning that). It was suppossed to be a quick mission (A 3 hour tour. A 3 hour tour.) But the displacement wave (The weather starting getting rough. The tiny ship was tossed.) was enough to overload some of the equipment in sickbay killing the only doctor and nurses with which they left. The large sickbay and multiple doctors, some of whom would have been off duty, on the 1701E would mean Picard would have had another doctor to make CMO. Remember CMO is a position, not a rank, so an ensign doctor could be the CMO.