There was an off-Broadway musical in the mid-60s called "Jo" that ran about 6 weeks. You'd have to check Theatre World.
There was an opera version done at NY City Opera very recently, last season maybe, that worked well. I believe it was televised and ought to be available at the Museum of Television and Radio if it is not available to rent.
My one concern about the source material is what will the conflict be? A love story with the insipid Laurie? Becoming a writer? Both?
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher