My opinion is, let it out! You said that your faith is very important to you and you'd like it to be a part of your future relationship. To do that, you will most likely need to date a Catholic - not just any Catholic, but a Catholic whose faith is important to her. Sure there are possibilities outside of that, but why go looking for a slim chance when you've got the opportunity to start out right? You are in a perfect situation - not just that you haven't started dating anyone yet, but also that you are at a point in your faith journey that it makes sense for you to be talking about it more than average.
The more dates you go on with a person, the more attached you are likely to get, and the harder it will be to break it off if you discover important areas of incompatibility. The way I see it (as someone who used this method of discovery when dating my now husband), the more important the aspect of the relationship, the sooner it should be discussed/addressed/discovered. This is because the purpose of dating is to find a spouse. Now of course, going on a date with checklist in hand is not the way to do it. But you should know what the major non-negotiable issues are for you, and it only makes sense to discover those things soon.
So bring it up. Don't go overboard, and don't ONLY talk about your faith. Talk about a couple of things that are important to you, and talk about a few things that aren't (just to have pleasant conversation - like you would with any new friend). And of course, ask her plenty of questions to give her the chance to let you know who she is. But definitely mention that one of the big things in your life is that you are going through the involved process of converting to Catholicism and how excited you are to be learning about and getting involved with your new faith. Ask your date what her religion is. Since it is close to Christmas, a good non-threatening question about faith can be about how she celebrates Christmas, or what Christmas was like for her as a kid.
One of 3 things will happen. ONE - you and she will find out that you're both religious Catholics (or almost Catholics) and you can connect on that level as well as continue to see if you are a good match in other ways. TWO - she will let you know that religion isn't very important to her or that it is important but she is a different religion, and you can enjoy the rest of the date but perhaps not move beyond friendship after that. THREE - she will like you less because of your enthusiasm about your faith. In this case, you will be lucky because obviously, she wouldn't be the one for you, and you won't have to let her down.