Dolomite itself is a mineral, and its discovery is not tied to a specific date.

However, it was first described and named by Déodat Gratet de Dolomieu in 1791. He found the mineral in the Dolomites mountain range in Italy and named it after himself.

So, while we don't know when the mineral was first "discovered" in the sense of being noticed, we do know when it was formally described and given its name.