Cowriting with someone who has Permission is OK; it's assumed that the person with Permission can keep the other one in check, if needed. Of course, if your girlfriend would want to write on her own, she'd need to ask for Permission for herself.

Okay, first of all, welcome back! Returnbies are always nice. ^^
Anyway, as for your question, I'm not a PG (and don't even have Permission myself) so this is purely in my own opinion, but I think she'd also need Permission. It's granted mostly based on your own writing skills, after all, and that doesn't mean anything about what your girlfriend's writing is like. If she's a good writer, I guess it would be easy for her to get Permission, at least! Though coming up with your own Agents if you don't necessarily plan on using them much might be a problem, I guess.

When I started writing PPC missions, I cowrote with a friend who didn't have Permission, but was allowed to as long as I was writing with her. There was a stipulation that she would have to get Permission as well at some point in the future, but she left before that could happen. I know we've had other, similar arrangements in the past, too.

So I'd assume the same would hold true for your girlfriend. Good luck! :)