A few ideas...
Depending on your child, The Magic Tree House series may be too difficult for a six year old to read independently, but of course, every child is different and your child may be ready.
Other series on the same reading level as MTH are Junie B Jones, Nate the Great, Captain Underpants (not my favorite, but it does get them reading), A to Z Mysteries, Cam Jansen, Magic School Bus (there is a picture book and a chapter book series). You didn't mention if you had a boy or girl, but the American Girl series is very popular with girls in the US--a boy from Australia may not be so interested!
Some other popular authors would be Beverly Cleary (Ramona and The Mouse and the Motorcylce), EB White (Stewart Little, Charlotte's Web), and Ron Dahl (James and the Giant Peach, Charlie and the Chocolate Factory).
Another idea to get them reading is to subscribe to magazines of interest--National Geographic Kids, Sports Illustrated for Kids, etc.