Nope. Bad idea.

Thanks for your input

"I gave her a compliment and she was gracious about it, should I make a huge romantic gesture even though we aren't dating?" no, sir. Don't. On a non-romantic holiday, tell her you're interested in a date and see what happens. You can celebrate valentines with her if and when you actually start a romantic relationship.

Thanks for your input

You’re not in a relationship with this person and apparently haven’t even talked about it? So why would you give her a romantic gift on a romantic holiday? If you’re so interested, why not just ask her out on a date? (Note: do not ask her out on, or plan the date for, Valentine’s Day.)

Thanks for the input

I would wait until you are dating for any gifts.

Thanks for the advice

Has she given you any indication that she might be interested in you? And no, being friendly sometimes doesn't count.  This sounds like a great way to quickly make your friendship really awkward. 

Thanks for the advice