Petrified oak slabs exist

"Petrified Oak Slabs" look identical to "Oak Slabs", however they don't burn, have stone sounds, and need to be mined with a pickaxe instead of an axe.

They used to be the only wood type slab available in the game prior to Minecraft 1.3.1 and were kept in the game as a Creative-only item because of backwards-compatibility with old pre-1.3.1 worlds.