A few months back I got a little help making my first whistle from Mutt. Now I'm helping thedecoydude with his first. I've received a number of PMs from folks about making them so I'm going to give you guys enough info to get started making your own.
First, I drill a 1/2" hole into my blank, probably about 2-1/2" to 2-3/4" deep. It isn't super critical, you just need to drill past where the 2nd hole will be. I use an expanding mandrel as a crush mandrel or you can plug the end and drill your hole all the way through so you can use it as an expander.
Then I turn the blank round and mark my holes. I do not use a drill bit to drill them. I use a chamfering bit with a lot of cutting edges. Irwin makes mine and it is a 90 degree. I insert a 1/2" dowel into the call so the tip of the bit is fully supported all the way down. The dowel also prevents blowout on the inside of the call and leaves a pretty clean edge. They tend to chatter, but if you drill at high speed with the call mounted in a vise (and go slow), it works on any material. Getting a sharp edge on the hole is critical. Simply drilling a hole and leaving it squared off will absolutely prevent your whistle from whistling.
Now that I've got my holes drilled, I put her back on the lathe and turn my whistle to shape. This is just like any call....You find a shape to make them look uniquely your own. The outside shape doesn't really do much of anything to the sound.
Here's how mine look when they're done being drilled and turned....I don't think they look like anyone else's on the outside, at least I hope they don't.