I used EK DXB to YYZ. We have a retriever as well and she was "checked in" baggage and not Cargo as the price you quoted was pretty close to the "pants pulling down" they tried to give me! If I recall correctly there was a fee of 500 USD or so but it was better than the alternative. You may have to consider DXB JFK or DXB YYZ and then connect to a domestic flight for the remainder.