It looks like Fantasia style. Fantasia was a Disney animated movie from 1940. You might like to see it, or a book about its art.
There is also a touch of Art Nouveau in your card design, but your card has a simpler and more elegant look than the usual Art Nouveau.
Just a suggestion:
This would look nice as a backlit Duratrans, but that would be expensive for you. If you want to experiment, here's an instruction page for just printing transparencies: