Should I ask her out on a first date?

I have been liking this girl for some time already and we have been talking for two months like twice a week for she comes in my class and sits next to me twice a week. Now we are having a centralised exam and high school is about to end. No more lessons so there's no chance for us to talk anymore. Well, i have not forged a relationship where we can talk right away when we meet yet. She is an introvert whereby i am similar kind too but i am a little more social. But i feel like progressing things after this centralised exam by asking her out to a game of badminton or a stroll at the park maybe. We are not that close yet and i am not really experienced with dating so i am wondering if it is appropriate to ask out a girl who knows me but are not close friends yet. Will appreciate help from you guys..
Should I ask her out on a first date?
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