Holy thread resurrection Batman!!
Hi Marick and welcome. Clearly you've cracked one of the biggest secrets in aviation forum posting, the search function. Good on you for doing that, it sure saves a lot of time for those of us who are happy to answer questions, just not the same one over and over and over.
I live in Dubai. Wife doesn't work and no pets so I'm probably not going to be much help. But yes, people have brought pets from the USA and yes the company has, at times, been accommodating to pet friendly housing requests. If you are married with kids you would get a villa/townhouse with a yard so pets are not an issue. If you do not have kids then you would get an apartment. In the past there have been some that are pet friendly, but very limited. That makes taking the housing allowance more attractive. Then you can find your own townhouse of villa with a yard and keep your pets.
You'll find spouses who love Dubai; who hate Dubai; and who tolerate Dubai. It runs the whole spectrum. It really is an individual thing. You're starting out right by doing research. Gather all the facts; make a visit then decide for yourself which you might be.
Typhoonpilot