Unmarried but want to baptize baby

My fiance and I have been engaged almost 2 years. About 6 months into being engaged and right as we started to plan the wedding we found out I was pregnant. The day after we found out a friend had suddenly and tragically passed away. With all of that going on we didn’t really want to get into the full planning process of putting together a wedding. Now my daughter is 7 months old and we really want to get her baptized. I still want to have a catholic wedding ceremony too. Would this still be possible even though it’s obviously not the traditional way to do things? Any one go through something similar?