Do nonrates stay at their first unit until they go to "A" school?
Yes.
What if a year has gone by and the wait for "A" school is still at least another 18 months or so?
She stays at the unit for another 18 months while she waits for "A" School orders. The typical afloat tour is 3 years.
Also what if the boat goes into dry dock?
The Command will decide what the crew is going to do. I have a friend whose boat is going into drydock soon. He'll be coming to my office TAD (Temp Additional Duty) I don't know if your daughter will have the same opportunity.
she is not real happy at this unit.
It happens. I wasn't too fond of my first unit until I left for "A" school. I left with more good memories than bad ones. All she can do at this point is make the best of it.