I'd say do it. You will learn a lot!
Besides, 20 is way too young to get married. I waited till I was 28! You need to live life, you need to live life being 21 without being married. You will both want this - trust me on that. You will feel like you missed a part of your life if you get married this early. In a few years, maybe you can get back together again if you want, but for now - you need to see the world without being hitched. Navy is a great way to do that, and learn skills and dicipline at the same time!
Chances are, when you go for a few years at this, you will see the mistake you were making. She left because she wasn't sure. That is the problem - you are too young to know if its the 'sure' thing. As far as I'm concerned, her breaking it off is probably the best thing that happened to both of you at this point, yet I hardly doubt you realize it yet.
Am I making sense? Don't be down on this. Look at it as an opportunity to find out what 'you' really want in life. When i was 20, I thought i knew it all, but I didn't know squat.
-S