I used an agency at both ends because I was terrified of something going wrong and the cats ending up at the municipality! But if you look at Dubai Kennels & Cattery (DKC) website they have an very clear section which sets out what you need to do, if you decide to do it yourself. Good luck!
Hey!
I am in Dubai for almost 3 months now and I want to bring my cat here. I have already arranged an agency at my home country (Turkey) and they will deal with all the necessary tests and paperwork. The question is, it looks like all I need to do is uploading the relevant documents, paying 500 AED and getting an import permit from MOCCAE website. Also on the day of the journey, I should go to cargo village and pay another 500 AED for examination. Is there anyone who went through this procedure without an agency? I am already paying a hefty amount of money on the other side and frankly, I am on a tight budget, so I don't want to pay another 3500 AED to an agency for something I can also do.