Children this age tend to be heavily focused on gender and The Rules of Gender. (Imo, it's worst when they first enter preschool or kindy, because now they have a whole bunch of other kids, all converging on a consensus of How Gender Works, and you'll be amazed what they know already.)
This is all very age-appropriate. This child is a girl, she knows she's a girl, and she wants to act like she thinks girls act. If you don't make a big deal out of it it'll ease faster. Think of it like the Bad Words phase (which, incidentally, this kid is running up to - they enter it around age 4, or, as I call it, the "eff you fours") - if you treat using bad words like any other small misbehavior, causing no more comment than "Let's pick another word next time", then there's no fun and they soon start using those words only when appropriate. But if you make a big deal out of it, they use them all the time.
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This is all very age-appropriate. This child is a girl, she knows she's a girl, and she wants to act like she thinks girls act. If you don't make a big deal out of it it'll ease faster. Think of it like the Bad Words phase (which, incidentally, this kid is running up to - they enter it around age 4, or, as I call it, the "eff you fours") - if you treat using bad words like any other small misbehavior, causing no more comment than "Let's pick another word next time", then there's no fun and they soon start using those words only when appropriate. But if you make a big deal out of it, they use them all the time.