I have a stutter and in a relationship. It really depends on the person. I was raised with my dad and brother having a slight stutter. I got it worse. But we were raised to embrace it and laugh it off. Not sure how your gf is. Maybe once she’s more comfortable about it and you can laugh about it. Because me and my gf laugh especially at restaurants when I’m trying to order and and there a million questions I.e soup , salad, dressing. I start to stutter and my gf will finish ordering because I get stuck and we start laughing