She is messaging with me but really doesn't come off as iinterested

Past two days me and this girl have messaged each other a couple times. I initiated the contact and to be honest, I would be very interested in meeting her. Well anyway, she always responds to my messages but she doesn't ask questions like i ask her. Part of me just wants to say screw it and not bother, but the way I see it, if she keeps replying there's gotta be some interest. Otherwise, why waste your time and my time?

Should I just keep chatting with her, and see where it goes such as Initiating a date after Christmas and see if she is interested? (I figure after Christmas would be better due to the rush to finish shopping and that). Or maybe just flat out ask her if she has any interest at all now?

Try dialling her number and talking to her.

Don't use text messaging if you are pursuing a girl to date. There's no class in it. That might be why she doesn't respond, you appear to have no class. Talk on the phone or face to face.