Jokes aside, the answer is YES, it is a common practice here to find pets (dogs/cats) in company provided accommodations.
You don't need any paperwork from Qatar state or the company.
Just ship with you and there is almost no vet check upon arrival.
I recommend carrying all necessary paperwork depending on your home country.
e.g. pet electronic ship, vaccination proof…etc. carry it with you, so it will be easy to travel back with it.