If you've never embroidered by hand, this isn't a good project to start on. Leather is completely unforgiving about stitching. Every hole shows. And a decent embroidery machine with downloadable (unusual) fonts costs more than $500.
It would be a lot cheaper (and easier and more professional) to take this to somebody who already has an embroidery machine, and can download the desired design/font onto their expensive machine. Look for an embroidery kiosk in a mall near you, or use yelp.com for your area to find the right small business.
If you want to attempt this by hand, practice on cheap vinyl from a sewing store first. Try to find vinyl or faux leather that has a weight and feel similar to your leather hat. You can simply draw the design on the practice piece, then fill in the design with short and long stitches. If the leather is stiff, you don't need to use an embroidery hoop.
https://www.youtube.com/watch?v=0FzU-DynaXw
https://www.youtube.com/watch?v=Ic6hve0QU-8