Hey, I'm new!
I would use either a nice yellow or orange background - soft. Not too bright or too dark. The hat is muted so you need something that will bring it out.
I also suggest adding images of a head model if you can such as if you have a baby or maybe ask someone who does if you know anyone. Or hang it over a bed post or railing post or something that will allow it to wear so you have a view of what it would like when wearing it.
You can also try placing it in a baby area - just make sure to not litter the area with too much baby stuff.
I hope this helps.
And try to get some lighting. Grab a lamp and take the shade off and photo with the extra lighting.
