My wife and I were in a similar boat in college. I was a tennis hacker who loved to play (not quite where you are) and she was an accomplished tennis player (star of her high school team from 8th grade on.) First some warnings: You don't want to get hyper competitive with someone you're dating. You're out there for fun and you're likely outclassed anyway, so no cursing, throwing rackets, trash talking. I've seen couples play together where I cringe with discomfort watching them on the court, even when they are on the same team. Not everyone can suppress their competitive fires enough to spare their partner when something goes wrong and partnerships where there is a significant skill mismatch produces lots of tension.
That said, definitely learn to play. Go out, have a good time, try your hardest and understand that she will thump you good. She should be in a good mood to go out afterward and you will be the butt of good natured stories. Play some mixed, but get an understanding ahead of time. Some people play mixed for the social aspect and some play to win. You need to know what you're doing. Mixed is a place where a guy can get a bad reputation quickly. Two things to watch for to see if you can keep it up: If the stories aren't good natured, that's a really bad sign. If you manage to win a set and she gets angry, that's another bad sign.