Well, all you've described is the purpose she needs to fulfill in the plot!
(So I assumed you were going for a plot approach to the problem, rather than a character approach. Not that a double approach isn't possible.)
*sniff* After I racked my brain to think of a female INTP for you and all: Enid in
Ghost World.
I'm sure you know a least one INTP female, at any rate, whether you know it or not. Maybe you just need to get to know one better? Or, I don't know- spend more time at INTPCentral.
Take all with a grain of salt:
What I know about INTPs: Can be "nerdy", can be slackers, can be geeky, can be cool. Can analyze things to death. Can be silly. When get angry/upset, might rant about how everything is illogical.
What I know about female INTPs: They sometimes masquerade as INFPs and vice versa.