I did a very similar transition, moving from wet lab biology late in my undergraduate career to computational biology, which is what I work in now. It's certainly doable - I made the switch with no programming experience whatsoever.
I don't necessarily know that the desire and knowing some Python is out and out enough to make someone confident of letting you dive head first into their project, but it certainly is enough that I'd ask around. You should be aware that a switch like this will probably cost you some time, but if you're okay with that, see if its possible to do a rotation in someone's computational lab - a semester or two for you to get the feel for what it's really like, pick up some skills, and hopefully either they'll pick you up, or "I did a rotation in Dr. So-and-So's lab..." being enough to make someone take a chance on you.
There are some other things you can do as well - follow your interest in computational work by replicating some classic papers in the field. Doing some side projects - computational representations of your current work, or implementing a commonly used algorithm on your own (say, the Gillespie Direct Method and it's many approximate methods). Things that will build your skills and suggest that you're worth taking a stab at. The other suggestion, if you can't effect a full transition, is to potentially propose one Chapter/Specific Aim/etc. of your dissertation as a computational project, and put someone appropriate on your committee.