Rabbit Wants a Rabbit

First, let us address the whole rabbit thing:
The young folk may not have heard of it, but Jimmy Stewart starred in a movie called Harvey. Stewart plays an aimless drunk who is friends with a giant invisible rabbit named Harvey. This, as well as my love of all things rabbitty, led to the well-enjoyed nickname, Rabbit.
Anywho, I'd love a meer shaped like a wabbit, but it'll be a looooong time before I can swing a comission like that. Plan B is to modify an existing briar. I've got a nice Foredom flex-shaft and was planning to use that to draw a rabbit head onto a yet-undetermined pipe. It won't be a detailed piece, just a line drawing of the rabbit's profile.
My concerns surround the bit: I'm not sure what sort of tool to put in my flex shaft. I've got a set of engraving bits for steel, can I use them on the briar? Wood is quite foreign to me, I usually don't work with materials that can't be melted.
Any guidance would be appreciated. Thanks!

I have worked with clay, but that was part of a one-off project and I have no equipment or material.
Actually, I'm proud of that project. Built a potter's wheel out of computer parts, an antique kitchen mixer, and some other junk. Made a couple of nice little pots with it.
But, fun as that was, it won't help me make a pipe. Perhaps in Minnesota I can use the art facilities at Shannen's university to make a clay pipe. For now, the briar engraving/carving is the plan.
Oi.

I'd seen those first two, but not the last one. That upside down head is freaky!

Also, in search of a pipe to rabbitify. Happy to trade for something smooth, no fills, with a vulcanite stem. Not totally sure what shape I want, so just send a message and we'll chat.

Oh geez, had a crush on her when I was a kid.