The Doedicurus can gather Obsidian, but only on specific rocks. Other creatures, such as the Ankylosaurus and Magmasaur are able to gather Obsidian from all Obsidian rocks.

From the ARK Wiki: [The Doedicurus] can gather obsidian from the rocks in the caldera of the volcano on The Island map, but not from the rocks on the last part of the way up to the caldera. On The Center map it can’t gather from the rocks on the shores of the lake under the floating island or in the mouth of Skull Island.