Do you think it is okay if I don't get my sister a burger at the canteen?
Why won't you get her a burger?
This is something I wanted to do just for me, not for her
Well, it may have been your idea and something you wanted to do by yourself.  However, since she's there now you should let her get whatever she wants.  Getting food for just you and not her as well is pretty rude.
She can get her own food.
You're just being rude right now, and you have to take a few minutes to collect yourself and think. How would you feel if you went out with your sister and she bought something for just her?