Due to its geography, Dorne doesn’t have much in the way of viable harbors, and Martell policy has historically been anti-naval as part of their larger cultural policy of forging a unitary Dornish identity. Moreover, a lot of their resources would be focused on the land-based threats from the Reach and the Stormlands.
However, we know they have some small naval forces, hence their intervention in Prince Daemon’s war for the Stepstones, their attack on Cape Wrath during the First Dornish War, etc.