It is very typical for kids to have a phase a baby talk and baby play around age three or four. Often it coincides with the birth of a younger sibling, but our child is an only and he went through the phase too.
My suggestion would be to set a time to 100% indulge it and really get into it. Have her sit on your lap, wrap her in a blanket and rock like a baby, pretend to burp her, etc. Play it up to an extreme of gushing about your baby. You may transition this into talking about when she was a baby and your memories of that happy time. As irritating as this is, trust me there will be years when you look back and wish she was on your lap rocking and pretending to be a baby. Our experience is the more we 100% got into it and thoroughly indulged this need the less he had it. I would try that for a couple of weeks and I bet you'll see it start to fade away.
