A "Chipmunk" might be too small ...
You're already talking about what to buy; and it's a rifle, not the mortgage on a house. GF or not, she's
a potential gun owner. Of course she's worth it.
When I was a kid, we used a Stevens Crack Shot; I still like to shoot them (but have a good gunsmith check the soundness of the metal if you find one of these). The modern equivalent is a Savage No. 30 "Favorite." Fit and finish aren't what they used to be, but that's fixable, and you won't mind altering the stock so much. In addition, there are a lot of old "boy's rifles" on the used market. An old Remington Model 33 handles like a dream, and it's quite small and light. Prices will vary, but these old rifles are nice options. Recall that, once upon a time, it was
normal for children to have and shoot guns. Manufacturers made a lot of short, light rifles to fit them.
{EDITED TO ADD:} And when she's ready to shoot a centerfire rifle, get her an M1 carbine!
When to do that is a judgment call for you to make. In my (family's) case, Dad got one for my mother (who's 5'2" like your GF) for Mother's Day when she was going to have their first child — me! Mom has told me that I went to the rifle range a few times before I was born.