I made mine from fondant. I added a little tylose to make it hard and allowed to dry. I used my Wilton double edge fondant cutter to make the seam around the brim, placed a rolled up paper napkin under what would be outside of the brim or the end not touching the cap. Worked well for me, HTH
I made a brim out of a 50/50 fondant/gumpaste mix. I gave it 2 days to dry and it wasn't quite long enough. 
It drooped when I put it on the cake and I had to shove a fondant ball under it to hold it up. It wasn't visible at all but still, not up to my standards. If I were to do another I'd make the brim several days to a week in advance.
I live in a very humid area, so I use straight gumpaste. I have an acrylic canister in my kitchen that is slightly tapered so that the curve is more pronounced on one end like a real hat is usually more curved on the outside edge of the brim. I put a good bit of cornstarch on the form so it won't stick. I roll the gumpaste about 1/8" thick so that it is sturdy. It takes a couple of days for the paste to dry enough to hold the shape, and I then transfer it to my dehydrator for a couple of days, so it is a week-long process. Also, make two. There will inevitably be problems if you only make one 
i made mine with fondant and candy clay mixed. Its in my photos. I cut the brim off from an old cap of my dh and covered it with press n seal. I used the brim as a pattern. Then traced the brim onto stiff cardboard. I then cut out with fondant and candy clay and layed over the real brim covered in press n seal. I let it dry for 3 days. hth next time , i will use g/p only. that will dry faster.
If you can get access to Elisa Strauss's book, Confetti Cakes, she has complete instructions for making a baseball cake, along with template for the brim. She suggest using cardboard shaped into a curved by folding in half and placing it on top of something round like an empty paper towel roll. She used gumpaste, make 2 days or up to one week before cake.
I had never made one before and all the folks on this website helped me with my first a couple of weeks ago. It turned out so professional looking. I did follow the suggestion of taking a hat and covering the brim in Glad PressNSeal...then I rolled out fondant and cut to fit brim and applied my lines using my fondant cutting (design) tool and let dry for a week...it was humid and still a bit soft that day. I used the sport ball pan (1/2) and a 6 inch round.
I recently made one also! It is in my photos. I used gumpaste but we are in humid FL. I dryed it on a oatmeal container covered in cling wrap. I let it dry for 2 days and that wasn't long enough but mu son doesn't like a big arch on his bills so it was perfect!
I made mine using gumpaste from the pattern in Elisa Strauss's book, Confetti Cakes and dried it on a piece of parchment paper on top of an actual hat brim. I gave it a week to dry and it did well. I did make a backup brim but fortunately did not need it. I have the picture in my photos.
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