Your original sentence is grammatically correct.
With short wings and a big beak, a toucan hops between branches instead of flying.
Here is a slightly clearer version you can use:
A toucan has short wings and a big beak, so it hops between branches instead of flying.
Easy steps to understand why this is good:
- Who is the sentence about? A toucan.
- What does the toucan do? It hops between branches instead of flying.
- Why does it hop? Because it has short wings (and a big beak).
Both sentences are correct; the second one just makes the reason a little clearer for young readers.