Can Malzahar kill an exhausted Gold to use his ability?

Yes, Malzahar can kill an exhausted unit (or gear) to pay the cost for his ability.

According to the FAQ regarding Malzahar:

• Costs can be paid in any order: You can exhaust Malzahar first, then kill the target unit (or gear) to satisfy the costs.
• Exhausted status: There is no restriction preventing an exhausted unit or gear from being chosen as the target for the "Kill" cost of Malzahar's ability.

As long as the unit or gear is friendly and on the board, it is a legal target for the kill cost, regardless of whether it is currently exhausted or ready.