question answered !

I have found out about the Dutch hat similar to the doll's hat I bought in Bruges.

Apparently it is a traditional hat from Gelderland in the Netherlands.

Thank you internet, and all the people who gave me advice !  If anybody can add more information, I would be glad !  This is what I found :

a baby cap with a star pattern was for a girl

knitting descriptions from the early 1900s

the first part is knitting a star

the finished hat.