I used to be a desert dweller. Many desert trees and shrubs have stickers or spines that will end up on the ground, so I would avoid planting those, since they will end up in your ducks' feet. Mesquite trees are shaped somewhat like an umbrella. They can provide a nice shape canopy, though you will have to prune and shape them and they are more likely than many desert trees to be blown over in storms. Some varieties may have thorns, so choose accordingly.
Acacia trees can be very nice and grow relatively quickly. They tend to be shaped more narrowly than a mesquite, though that varies with the variety. There are numerous varieties to choose from. Some may have thorns.
Desert willows (the silver leaves with purple flowers someone else mentioned) are nice, but slower growers that are really large shrubs people often prune as trees. That's true for a lot of low desert trees.
If you have a way to water them adequately, citrus grows very well in the desert, though I don't know how good citrus is for ducks. The tree trunks have to be protected from sunburn.
For a large, tall-growing shade tree, consider an Aleppo pine. But be careful to plant it far enough away from your foundation slab and your block fences because their roots can undermine them over time. Arizona ash trees used to be a good shade tree choice, but ash borers and disease were wiping out all of the ash trees in our neighborhood before we moved away.
There are a lot of choices of desert shrubs. Purple or red sage do well, as do cassia (yellow flowers), and the desert varieties of bird of paradise. Globe mallow has coral colored flowers. Avoid creosote! It is probably toxic to ducks and it is definitely toxic to other plants around it.
Bougainvillea is pretty and grows well in the desert, but has thorns. Some varieties have fewer than others.
I don't know whether any of the plants I've mentioned present a poisoning hazard to ducks, so you will have to check that out.
Gravel, sand, and even dirt can get very hot in the summer. Do not choose a dark colored substrate because it will absorb and radiate heat. Also, if your home has scorpions, you will want to avoid using a substrate that they find hospitable. If you have them, they can be hard to get rid of, though fresh cedar mulch spread in the places they are breeding is said to be helpful. The cedar oil is reportedly lethal to baby scorpions and deters adults. Some people find DE helpful. The biggest help is eliminating their food source, which includes crickets. They are not very affected by pesticides.
While you wait for your landscaping to grow, you may need to construct some shelter for your ducks. Make it sturdy enough not to be blown away by summer storms. I've seen patio umbrellas sail by 300 feet in the air. Also make sure it isn't inviting to black widow spiders.
The desert is a really different place than the Prairie where I live now. After four years, I'm getting used to not having to flip everything over before picking it up to avoid black widows and scorpions.
I would plant bushes. Then they can hide under them all year round (wind/rain/sun & hawk protection). Look for native varieties that don't take too much water or maintenance and you should be good. 
