There are a few magical academies around the Inner Sea where wizards graduate at second circle, sometimes even third, but you couldn't have paid her to go anywhere near one of those.
"More education after learning to transcribe and hang first-circle spells is optional. The Arcanamirium has specialized curricula for students at higher circles, but the real draw is getting to swap spells and collaborate with other students. You pay your tuition, you get subsidized magical ink and a friendly environment. It's faster and safer than working alone. The headmaster will give you another diploma if you ask for one, I think."
The postgraduate study benefits extend to surprisingly powerful and accomplished wizards. Novitiates at the Arcanamirium can enter something like an apprenticeship under older students, with the faculty theoretically serving as a bulwark against the worst sort of depredations, and active students get priority enrollment at colloquies held by senior academics from other universities.
"One of my fellow students tried to involve me in a series of questionable life decisions over the years, which wound up being, ah, mentally and financially taxing. I got my commission as a way of leaving Absalom for a few years. Third circle gets you into the officer corps immediately, but it's just junior enough that they can't risk me on any of the terrible jobs, like search and rescue in the Cairnlands. My service has been… relaxing. Maybe too relaxing."