Let me give a few words of advice here to help you in the right direction. One of the first things about learning trumpets is to understand how they work. Yes seems pretty simple all you do is suck air thru the call but nothing is as it appears especially in the call making. When air is drawn through the tube a certain amount of moisture is transferred to the mouthpiece and call. When this happens it will cause the wood to expand and swell. In the case of the mouth piece being made of wood it can have a adverse effect on the sound of the call as the hole closes up. As time goes on it will cause the call to be more difficult to draw air up the tube and render the call useless until it dries out. Now you may think if you make a large enough hole in the mouth piece this would lessen the factor. True but this will cause the trumpet to have a less than desireable sound and cause the user to have to draw so much air thru the call you'll black out trying to get the notes you want to sound like a turkey. You will want to make your hole in the mouth piece from 1/16" to 3/32" dia. The smaller the hole in the mouth piece the higher pitch the call will exhibit, the larger the hole the sound will then deepen and require a little more air to draw thru the call to get your sounds.
The idea on the trumpet is to have nice smooth transitions when making the tube or the mouth piece so you will need a smooth tapered reamer to hone your trumpet body internals. Your mouth piece will be a straight thru hole with no taper. Mouth pieces are normally in the range of 2 1/2" to 3" in length with 1/2" glued inside the trumpet barrel.
The call bodies should be made from a wood that will remain rather water resistant such as Stabilized woods, Cocobolo, Lignum Viate, Ivory, Acrylic, Delrin and the likes of those. Refrain from trying to finish the inside as each time you draw air thru the call you will taste the finish that you used. After a few tries you'll figure that one out on your own though.
There are tons of materials you can use for the mouth pieces and to give you some ideas here is a list of items I have use in the past, Acrylic pen blanks, Metal such as SST, Brass, Aluminum, Bone such as Turkey wing bones, Goose wing bones, Duck wing bones, Beef leg bone, Camel leg bone, Giraffe leg bone, Buffalo horn and even Deer antler but it must be of solid bone composition as most are quite porous, Delrin plastic and even Cane if found will a small enough opening. Back in the day Cane Yelpers were widely used for turkey hunting all made from cane fitted into each other. Let me know if this helps you at all and don't be afraid to ask us here!
Larry