You can check the dog in cargo as long as the summer travel embargo for animals is not in effect. The last I knew, the embargo began on May 15 and ran through September.
Check when you make the reservation. Be sure to ask.
One time I traveled here to the DR, had a reservation both ways for my dog, but when I tried to check in to go back to the US, I was told the embargo was in effect and the dog could not travel. Luckily, he is small enough to fit under the seat in the cabin, and with some scrambling, a friend was able to quickly get me a Sherpa carrier.
Good luck.
Lindsey