Hi SAPF and welcome to LWL!
Don't worry about getting too bulky like all those

hunky guys -- we women usually can't get like that (even if we'd want to) because we just don't have the hormones for it. So keep lifting and you'll end up with that lovely, lean muscle when you get to goal (and it will help rev up your metabolism so that you get there faster ...

).
About how much protein you need -- you'll see lots of different recommendations, so it can be confusing. I'm no nutritionist, but the one that I go by is one gram of protein per pound of goal weight (
not current weight -- that would be way too much). For me that's about 135 g/day, which is about what I average (and feel very good at). For your goal of 125, that would be 125 g/day.
I don't know much about protein sources in vegan diets but I imagine that you can get adequate protein from a vegan diet with some knowledge and meal planning.

Do you track your food now with Fitday or something like that? Do you know about how much protein you're currently eating?