I know how it looks. Don't overthink it. She's probably not used to this situation, but the fact is that she's interested to have a date with you, knowing you have a stutter. I laugh at my own stuttering too, it changed my life a lot to do it. If you laugh at your own stuttering, it will bring a good atmosphere, don't focus on it too much. Speak about various subjects, show your curiosity, especially about her, show your sense of humor, and more than everything, be yourself. You both could end up having a fun and nice date, it's just a question of mindset. If she's not the right one for you, then it doesn't matter, you'll find a better girl next time.