What is this - an old pipe?

This item was just inherited from my father-in-law. It looks like an old merschaum pipe or a cigarette holder, but it also appears to have wood grain-like striations in it. The surface is very smooth with a light gloss to it. The piece measures 2.25" long by 1.375" tall. A finely carved stag is leaning against a tree on top. A small stem (0.125" dia by 0.25" long) appears to have screw grooves or perhaps just plain circular grooves for something to attach to. The "bowl" is 0.5" dia and about 0.5" deep with a conical shape. The outside color is light brown with a darker brown in the interior of the bowl which might indicate smoke residue of some sort. The object is housed in an old leather covered case with a latch for closure. There are no visible manufacturer marks on either the object or its case.

Does anyone have any idea what this is? If you have an idea, might it have some value? Thanks for whatever help you can provide. Frankly, I am stumped.