Hi, I moved to DXB earlier in the year. We also brought out our dog. I used the DKC to handle all of the Dubai end, it cost about £400 after EK discount so not cheap but the doglet arrived in the middle of the night and DKC picked him up and kept him until the following morning. It is possible to do the whole thing yourself but it is much easier to have them handle the DXB end. We handled the UK departure arrangements. They were simple.
Regarding the cargo allowance, I asked the question at the time. The answer is that EK do not consider a dog as personal effects so no you cannot include him as part of your entitlement. You do however qualify for a 25% staff discount on EK services.
Hope this helps.