I agree, you two are still getting to know each other. It is way too soon for marriage. Or kids, so be careful with the birth control.
What kinds of things are you two fighting over? If it is trivial stuff, then you are both struggling to control the relationship. If it serious stuff, then maybe you two are just starting to discover that you aren't compatible. Don't think about fixing the relationship, just focus on discovering if there is real compatibility beyond mutual infatuation. Otherwise, the infatuation will eventually fade, and then you will discover the real relationship, which might be a bad one.
The whole point of dating is to determine compatibility. It can be tempting to rush through the dating, to quickly arrive at a happy relationship. Usually at least one of the two people has the common sense to proceed with some caution, because bad relationships and breakups really suck. In this case, you both rushed past the dating stage, leading to your current troubles.
Good decisions come from experience. Experience comes from bad decisions.