Pom isn't an insult down under, more of a description - a fairly standard term (though slangy) for a Brit, particularly one from England. The vast majority of people are either Poms themselves or have great-grandparents who were, so it is indeed banter, not a slur.
But it was still boorish of the teacher. Even if she'd said 'Oh no, not another English girl', it would still have been a rude introduction for a new girl. If anything like that happens again, a quiet word to the headmaster/mistress would be in order.