I also used Mersant International, coming from the US. They handled the docs stateside. You can use DKC on the UAE end (for a fee), but we opted to pick up our animals directly from the Cargo terminal after the flight. Took a couple of hours plus a few hundred dhs but was worth it for peace of mind.
There's a ton of paperwork, vaccinations, etc needed before you even ship them so give yourself plenty of time. I think you can find what you need on either the dkc website or uae ministry of agriculture (?).
Good luck