Don't overthink it dude. Overthinking only makes it 100 times worse! Its the worst thing a stutterer can do. I know its hard, I was once in your shoes, but you need to just take a deep breath and say whatever it is you want to say to her. The fact that she said that she doesn't care about your stutter should be a confidence booster because its showing that she has interest in you. Everything will be ok man just be cool. Edit: Also, if you're having a hard time keeping the conversation going just ask questions. Questions are your best friend! It took me a long time to realize this, its so simple. Don't over think the questions either, just be casual. Ask her how her day went, what she's doing, ask her if she has any plans for the summer, what she likes to do on her free time ect. Keep it simple. This will help you get to know her and it will show her that you care too.