My vote would be yes. The PB isn't really about weight loss, though it helps a lot of people do that. It's about being healthy, putting the correct nutrients into our bodies, eliminating the toxic stuff. Frankly I think the biggest selling point of the PB is the increase in energy most people get, which it looks like you'll need!
Try googling both "vegetarian" and "breastfeeding"... though not at the same time! I know we have had many threads on both breastfeeding moms and on people moving over from being vegetarian. There should be some really good info on there from people that have already been there and can help.
I don't have a lot of info on underweight, but my feeling is slowly your body will get to whatever equilibrium it wants to be at. For some people that is on the thinner side, but if your'e getting all your nutrients and get your system back to where it should be, it should definitely be healthier.