Need some dating advice.

Need some dating advice. So I have a huge crush on a girl in my class but I don´t know if I should try to ask her out or just leave her alone I just don´t want to embarrass her around others, I mean our first encounter was already pretty awkward I tried to introduce myself but I stuttered really badly midsentence but we just laughed it off (made a crappy joke about my stutter) but even after this awkward moment she still smiles at me every time we lock eyes. She also tries to make me speak more which feels good. So what would you people suggest? should I go for it?