Do I keep the family Apple Music if I change payment accounts in family share

I'm not sure I understand. If your dad is the Family Organizer, then he should (and must) be paying for the Apple Music Family subscription. If he wants to change his payment information, then he should see:

Change, add, or remove Apple ID payment methods - Apple Support

Changing the payment type should not affect the subscriptions.

If he wants got cancel the Apple Music Family subscription and you want to start an individual subscription. Then he should cancel BEFORE the next subscription billing cycle ends. Then you need to subscribe before that also to retain your music library. See the 'About canceling subscriptions from Apple' section in:

How to cancel a subscription from Apple - Apple Support