You can buy the branch perches from a pet store, too.
I looked up about budgies and eucalyptus trees and it says that eucalyptus is great for budgies. They are:
1. A toy for your budgies to chew up
2. Great natural food source
3. Great for building up a budgies immune system
4. Budgies like to bath in the wet leaves
5. Great way to get rid of mites in the nest box
6. When the bird preens itself after eating the leaves it rubs the oil through its feathers and gives it a nice healthy shine as well as a great way for keeping mites of our birds without using the spray stuff from pet shops.
That was from
http://forums.budgiebreeders.asn.au/index.php?showtopic=17915 by someone named Cara.
Where did you hear about eucalyptus being poisonous to budgies?