Before you get too carried away with the breaker, I would clean out
the lint from inside the dryer. 15 years of lint could be making the
old thing work just too darned hard.

You could also check for loose connections on the breaker. I replaced
my fusepanel with a circuit breaker panel recently. A couple days
later the dryer started tripping the breaker. Turned out I had
forgotten to tighten one of the screws, so the breaker was developing
excess heat.

Mr Fixit eh