The best local handicrafts are Carib made baskets. The earth tone colours come from burying the fibres in the ground for different lengths of time. All visitors need to ensure that the materials from which they are made allow them to be taken back home.
Dominica is also well known for its music, so be sure to buy some local music while you are on the island. Genres range from jazz, reggae-dancehall, calypso & soca, to Cadence-lypso and Bouyon and which are popular Dominican genres. Visit during the last weekend in October and be treated to the World Creole Music Festival (http://www.worldcreolemus...) or if you can't make it, ask for the best local artistes, and be aware of pirated copies!
Many kiosks and vendors line the shore at the main cruise ship dock. One excellent leather store faces the dock on the other side of the road. Just a short block inland lies a packed, open-air market with perhaps the island's best selection of souvenirs.
Look out for cacao sticks to make cocoa tea as a nice souvenir to take back home.