Making the hat was quite a task!
At first I wanted to make it out of plexiglass, but after visiting several plastic stores I thought that maybe vinyl would have been better and much easier to model.
But I wasn't convinced so I walked around the neighborhood to look at the junk that people throw away in the streets hoping I might find something interesting to use.
There was everything in the streets except for something useful for my hat. So I just picked up some ordinary cardboard to make the hat.
As you can see from the image, I started off with a milk bottle to keep the cardboard in place. 
Then I found that a bucket could be much better for this, so I got a bucket and made a brim out of cardboard, adding (later) other cardboard on top of the bucket to make the top slightly bigger than the bottom.
Now that I had the shape the best thing to do to make it weatherproof but also children-proof would be to use the shape as a mold and work the fiberglass on it. So that is what I did. It took me a whole morning and the result wasn't too bad... except for... the size! 
Only after making it and placing the hat on the dog did I realize it was far too big. It really didn't look proportioned so I decided to do it all over and it turned out pretty well.