I agree with Howdy that it seems more like an issue with the school/class management. Your description seems to show that the school has embedded a huge importance on age relative to grade that the other children are reflecting back.
We started DS at a local private school right as he turned 4 into a class where most of the kids were turning 5... but no one said a peep to him about age. We got that at his daycare, with the older kids making a big deal of DS being younger (who was 3 then) among the 4-5 year olds (he hated the 3s room and wanted to get out of there so daycare moved him into pre-k, and pre-k mixed with the private k class all the time). However, his current school downplay age - their stance is that if you are placed into a class, you belong there. His teachers are aware he is a lot younger, and they are aware of his developmental path relative to his age as being appropriate but do not see that as a reason he does not belong there. In fact, other than when the birthday party invitations come out, I don't think the kids really pay attention to how old their classmates are or age of the kids they play with at recess and before/after school.
If it is indeed a cultural aspect of that school, you may not be able to get away from that easily. And your DD's disinterest in the Kindy teacher going on leave would be a concern for me as a bad fit. My DD (3.5), when she does not like someone, will just shutdown and withdraw (and then take it out on us at home). For my DD, how she views her relationship to a teacher is very important. We have been lucky so far that those experiences has been limited to sub teachers or outside activities - but those times really has made me aware that if we get a bad personality fit, she is going to be withdrawn and she will just not perform (she most likely won't act out in school, but most likely will just not put any effort into her activities either).
