Can I get married in a catholic church?

You can certainly marry in the Catholic Church after you have been baptized. I don't know what point there is to taking the "quickest way." Especially since Jesus told us to "count the cost." It makes more sense to receive proper instruction and be sure of what you are getting into before baptism. Also, it makes more sense for the pair of you to be part of the same Church. So, I recommend taking Catholic instruction so you can be baptized into the Catholic faith. They might let you marry before you are done with classes, but even if they don't, it's time well spent. Also, you might be able to take an accelerated course privately with a retired priest or her pastor or whomever has time. She should take the classes with you as a refresher course.