To the op,
I know exactly what you're going though. At the beginning of 2012 I started a new job with a new hospital (rn as well). While I'm not in a probationary period anymore, I have limited vacation time and am not eligible for FMLA.
Anyway, our organization has a medical leave available at our managers discretion. While it isn't perfect, that's the route I've decided to take. Additionally, I've been open with my manager and am having surgery during the summer when census is lower and after more people will be trained for our shift. As a newer employee I'm trying not to make my surgery a burden for my coworkers or the floor.
As far as the amount of time you're taking off, you're not counting for any complications, giving yourself time to adjust to your new stomach, etc. This is major surgery. People with gallbladder surgery take off longer than you're planning or thinking, fwiw.
I'm not trying to be a downer, but Im just Concerned nurse to nurse. If it is any help, my surgeon lets some people go back after a week but after he learned I was a nurse and what kind of floor I worked on (med-surg/medical detox), he told me 2.5 to 3 weeks.
Best of luck.