I just finished knitting a baby hat with ear flaps using self striping sock yarn. It is adapted from an adult size pattern with a few minor modifications.
The brim is garter stitch and is joined with a stockinette top knit in the round. Super easy and very little finishing. You could sew a bow or flower to the brim for a more girly hat.
This will be the ideal hat for donating to a local hospital. The one I made would easily fit a large newborn to several month old infant. I am going to try for a little smaller size that would be suitable for a premature infant. NICU nurses (and parents) like the tiny sizes as they are especially useful for keeping baby warm once the warmers are turned off and baby is transitioning to room temperature.
The original pattern can be found on Ravelry as “1898 Hat”. This pattern has a double layer brim to keep your ears toasty. I did not do that as I felt that was too much bulk for a baby, unless you live in a colder climate than I do!