Need help making a shallow, oval-shaped beanie for a plush! Do I have to work in an oval or can I work in a round?

Hi! I’m trying to make a beanie for a friend’s plush, but the toy has a shallow, oval-shaped head that measures about 52cm/20.8” in circumference and about 8cm/3.2” from the highest point of the head in the centre, to the top of the eyes where the head is supposed to end. I tried to make a standard round hat but obviously the measurements I use for normal human heads doesn’t fit because the plush’s head is so shallow.

I thought I would try to make an oval hat but realised I don’t know how to size hats that are oval and couldn’t find any sources online (probably because humans don’t have oval heads 😭). If I make it in an oval, how long should I make the chain and how do I know when to stop increasing? Or is it somehow possible to work in a round?

Would appreciate any help on making a wide, shallow beanie, whether round or oval! Thank you!