We are likely to move to Dubai in the coming months and will be moving with our dog. We are keen to know if pets are allowed in motor city apartments since we plan to stay in that area. Also could you recommend options for short term rental where we can stay with our dog?

There is no rule banning dogs in Motor City however you would need to check with the individual  landlord you would be renting from.  Short-term rentals such as serviced apartments that accept pets is much more difficult to find but I recommend you try the Dubai World Trade Centre Apartments.