Australian plants do well in Arizona, as the climate there is similar to ours. Most desert gardens have at least three or four different varieties of "Aussie" natives. In my garden, I have several types of Emu Bush, Willow Acacia trees, and some Dwarf Bottlebrush shrubs, (Callistemon viminalis 'Little John').
The Dwarf Bottlebrush is a low mounding shrub that grows very slowly and will eventually reach about three feet tall with a five-foot spread. Since I don't want my shrubs to be sprawling, I prune them minimally in late autumn. They have attractive foliage and a bottlebrush-like red flower that blooms in early spring, then periodically through summer. Hummingbirds love them, but are sometimes hesitant to swoop in so low, so will choose other flowering plants before this one.
There are a couple of problems with the Dwarf Bottlebrush. It seems to collect more dust than other plants in my garden, so it always looks dusty. I think that's because the leaves are somewhat hairy. Although it does well here, it prefers a more humid environment where it can really thrive. It is also somewhat frost sensitive. Every year, I have to trim back a few frost-damaged tips, but even the hard freeze we had this past winter didn't severely affect it.
This little shrub is like a miniature version of the Bottle Brush Tree--same flower, same foliage, and same frost sensitivity. Like the Bottle Brush Tree, the pollen is an allergen, so sensitive folks may want to skip this shrub, as well as the tree.