Don't get too wrapped up in the Catholic thing. They also taught you not to have premarital sex. You can't cherry-pick what parts of Catholicism get to drive your decisions and what parts don't.
Also, you know well that early in recovery doing anything stressful is to be carefully, carefully considered, and few things are as stressful as marriage (and the baby, blessing that he/she is, never-the-less comes with stress).
What's most important is your sobriety because without that there is no potential wife, there is no child in your life, and there is no marriage. What's important after that is the child. What's important after that is your girlfriend. What's not important is marriage. And, in my opinion, there is only one reason to marry a woman-- because in your heart of hearts you want to share the rest of your life with her-- to be her husband, and have her as your wife.