The new species and name was confirmed in a scientific paper, external published on Monday.
Mr Simpson said the island's eroding coastline meant the fossil would have been "washed away and destroyed if it had not been found by Daisy".
Mrs Morris, a teaching assistant, said: "She has a very good eye for tiny little fossils and found these tiny little black bones sticking out of the mud and decided to dig a bit further and scoop them all out.
"We are all very proud of her".
The pterosaur has since been donated to the Natural History Museum which recently named the Isle of Wight as the "dinosaur capital of Great Britain".
The confirmation of Vectidraco daisymorrisae comes a week after the discovery on the island of an almost complete skeleton of a 12-feet long dinosaur.
Pterosaurs were flying reptiles that lived in the same time period as dinosaurs, up to 220 millions years ago.