Totally doable, totally fun. With an 18" tree you're not going to open a commercial mill, and depending on your purposes, you might want to use the wood more creatively than trying to mill it into standard lumber. You're looking at maybe yielding 60 board feet assuming you've got a pretty straight main trunk of 35 feet. If you went to the lumberyard that might be $240 for oak, less than a chainsaw costs. But if there's some interesting grain you could find the good bits when you're bucking it and turn some bowls and vessels on the lathe. You could always buck it into longer sections and carve some simple high-backed chairs with pieces. You could also split part and use some rounds to make rustic benches. Or if you think it would be interesting to learn, and want to buy a chainsaw, Alaskan mill and a peavey, you could try milling it. At 16" assuming 1" for bark you'd have material for live edge shelves, perhaps a fireplace mantel, you wouldn't have enough for a bookmatched table but maybe a rustic outdoor kitchen countertop.
Bottom line, cheaper and easier to go buy wood, especially oak. But if you're interested as a project, rustic hipster stuff is easy to make.