A 60 cadence for climbing a 9% grade isn't bad. Overall being new to cycling your regular cadence of 100-105 is a bit high. Several studies exists on cadence and generally 85-95 is good for most people with normal riding. Your high cadence riding along with low climbing cadence makes me think you need more leg strength.

I wouldn't bother your current gearing for a while. Use hills as a way to build strength. Stand occassionally and pick up the speed/cadence. Also use a more difficult gear on the flats and work harder in spurts.