If she shows an interest in music, I see no harm in pursuing it.
I agree!
Both my kids play music. They may or may not make a career out of it. It doesn't bother me. My wish is that making/playing music will always be part of their lives as I know of many children who gave up playing when they reach adulthood.
DS has perfect pitch but he doesn't like to practise! There was a period when he played the piano non-stop (really! first thing in the morning still in his PJs) for 3 months. After that, he was back to "normal". It was his first piano teacher (who is trained in special education) who mentioned that he has a gift. His current teacher teaches music theory too which is what he likes now. Few months ago, I was almost ready to stop his piano lesson but we came to a compromise that the lesson will focus more on theory and he will have lesser pieces to practise. I know I am probably not doing "enough" to develop his music talent but the last thing I want is to kill the interest as there are so many things which interest him now (Lego, Math) which takes up his time too.
So I will say go ahead because learning music cannot be wrong unless the child shows great resistance.
edit to add:
I would like to recommend this book "Raising Musical Kids: A Guide for Parents by Robert A. Cutietta." It has some wonderful tips on how to choose the first instrument / teacher, good practise methods and how school can help etc.
