It should work if you start with a baby-sized regular hat--maybe starting with white furry yarn, and when you get to the crown, put a few rows between the decrease rows--you'd get the longer point.
Here is one for preemies which you could make with more stitches, or ones for adults you could make with fewer stitches. I used the lionbrand one (I think*) to make an adult hat and two kids hats. I also made one for the cat. :teehee:
*they require a sign in and I don't know where my number is. I made them with chenille yarn.