What kind of dinosaur is ducky?

Yes they are.

The new phylogenetic classification system seeks out to classify by relationship and not solely charecteristics as the old classification system.

This means, if birds are more closely related to other dinosaurs, than all dinosaurs are to eachother, they will necessarily be dinosaurs themselves. Birds are more closely related to theropods, than they are to sauropods, and as such we can conclude them to be dinosaurs.

Source:

PhyloCode