Just started dating my roommate. Now what?

I (22M) moved into a new apartment mid-August, and am living with 3 other flatmates, one of whom (23F) I have become good friends with over the past few months. We started having romantic feelings for each other, and as of a few days ago, we have just started dating. As of now, we've basically been hugging nonstop all weekend, and that's the main difference between when we were friends vs. now, but obviously won't be able to do that during the week, since we both leave the apartment during the day.

But aside from that, what should dating my roommate look like? Neither of us want to have sex (for religious reasons), so that's not a difference. But what else can we do together to make it more than just being good friends? I'd take her out on a date, but where would we go during Covid?

I've never dated anyone before, so not sure if there's any 'should's here on how to make this work.

(Also, every sentence here was an oversimplification, but you don't necessarily need my whole life story in the OP, so can provide more details in comments where necessary.)