If you have the luxury of a little more time, I would suggest spreading the joy out over 2 or even 3 days. Walks of Italy's Pristine Sistine tour combines the Vatican Museum with St Peter's, and, even with a very early relatively uncrowded start, I find that a lot to cover in one visit. The Wednesday morning outdoor audience with Pope Francis can be very meaningful, and you can arrange for tickets online about 6-8 weeks ahead. The Scavi tour, which takes you underneath St. Peter's in a small group with a Vatican archeologist, is fascinating. You can also apply for tickets for this online a few months ahead.
All these suggestions are from life when it was normal, and hopefully when you go in September, maybe normal will have returned. There's so much to see at the Vatican, and it's also hot as blazes in Rome in September. Vacation days can be more enjoyable if you can mix the intense sightseeing with more relaxed cafe-sitting and people watching and get out of the hottest part of the day. Your girlfriend also might like to visit one of the catacombs out on the Appian Way, to get a feel for the earliest Christians. The Catacombs of St Callixtus offers a good tour, and it's underground and always cool! Check for tickets on line.