Your situation is pretty similar to mine both currently and when I first moved in together with my now wife. Congrats on the big decision to live together - it is better overall provided there is enough space to not drive the both of you crazy.
My wife is also a teacher, will be receiving a mid six figure inheritance (I will not receive anything within two orders of magnitude, if at all), she grosses in the mid 40s, and I'm in the low 110s. I've never done 50/50 on rent/mortgage and our finances aren't split down the middle on other things either. Also, there is a big difference between gross and take home, especially at salaries below the median household income level that are significantly contributing to retirement. While unlikely, your girlfriend could easily have $0 take home pay as a result of 403b, 457, HSA/FSA/cafeteria plan, pension, fed/state/local tax, and FICA. You could max all of your retirement accounts and pay taxes and still have more in take home pay than she grosses.
If 50/50 works for you, great. It doesn't/wouldn't for me. My wife doesn't come close to maximizing her retirement accounts each year and her box 1 on her W-2 is in the mid 20s. If our arrangement were to be 50/50 on expenses today, then she'd have to sacrifice more of her retirement contributions (and I imagine our spending in retirement would be more slanted to my side). I don't want that at all - I want her to continue to increase her contributions to retirement each year* while paying a proportion of household bills that we've agreed upon.
*-She's never been the one that's into finance but now after a few years she loves getting the annual reports from her school district with projections and her account totals as it grows and she knows that's it only been her shoveling the money in.
Oh, I'd ignore her inheritance since she isn't touching it and it seems like it's earmarked more for "down the road", just like retirement accounts. A lot of this talk assumes you're going to be together long-term as if you're married. When my wife and I moved in together, we were engaged later that year as it was part of the plan. If you're just testing the waters and still not sure if she's the one, then definitely do 50/50 until you have a good idea who you want to spend the rest of your life with. Talk it over and see what arrangement works best, good luck OP!