It shouldn't. You could always call the airline and check, but I asked once when booking my sister's flight...she was recently divorced and I didn't know which title was used...and they said they didn't care about that, just her name.
I don't remember if I had it right or not, but I do remember there as no issue.
Now, your girlfriend might think you're proposing, lol.
Here in Germany nobody knows what the difference between Ms and Mrs is (or that Ms is an option at all) and even on my very first plane ticket (to California in the 80s) when I was a teenager it said Mrs. on it. I would have been a child bride... So I am sure it does not matter at all!