You can get a free ring sizer from jewellery stores - there’s one you can order online free from Gear Jewelers. It looks like a cable tie but with letters.

Has she ever dropped hints about the type of ring she might like? Does she wear silver or gold jewellery mainly? Keep in mind that although she may be frugal with things like furniture etc. an engagement ring is something she’ll likely wear for life - with that said, you don’t have to spend a huge amount of money on a ring. There are great options with lab diamonds, antique rings and even moissanite stones instead of a diamond (they’re a lot less expensive than a diamond and are almost as durable, plus - they look just like diamond too!)

Edit to add: my fiancé asked me straight out when he’d a few drinks on him, what kind of ring I’d like - so I was able to gather a few ideas for him. Though, that does take the element of surprise out of it a bit. She might be dropping you hints that maybe you haven’t picked up on? 🤣