Is there a certain level of musicianship to be acquired before a person even attempts jazz?
I don't think so, no.
From your post, i would say that you are probably playing at a higher technical level than me, and i've started playing jazz piano. I've been working from 'Beginning jazz piano' by Noah Baerman, and am working on it in parallel with alfred all-in-one piano, book 2.
I think you may be starting out a bit too ambitiously:
Are you comfortable playing from a lead sheet?
Are you familiar with different styles of voicing 7th chords?
Can you improvise within a blues or pentatonic scale?
Compared to the alfred book, i'm finding the jazz playing requires more theory and thought away from the keyboard, so (for me, anyway) theres quite a bit i would miss trying to pick things up by ear that are more easily learnt from a book.
hth,
kevin