Should I be asking her the "what are we" question?

We have gone on three sorta "dates," which are mainly dinner and a movie, and we have alternated paying in full. But not once have we ever called it a date, nor have we ever got into hand holding or anything like that.

Every time, when I'd drop her off, she would text me later and thank me for giving her a fun time.

Is this a wrong time and place for me to ask her the "what are we" question?
Should I be asking her the "what are we" question?
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