It can be confusing when using common names for plants. Just look at Bird of Paradise. There are at least four different desert-adatped ones that grow here. That's why its a good idea to write down the botanical name and take it with you to the nursery.

Yes, Indian Laurel is the same as Ficus nitida. They are members of the Fig family and even produce tiny non-edible fruit. These trees are not considered low-water use and in the winter of 06/07 thousands were lost to the cold temperatures. They become huge trees and produce deep shade, which can prevent grass from growing underneath. They are also notorious for lifting sidewalks, pool decking and fences with their roots.

Depending on what size tree you are looking for you could try a Mastic (Pistacia lentiscus), fruitless Olive (Olea europea), or even a Sissoo (Dalbergia sissoo).

I hope this helps.

Here is a link that might be useful: Landscape Plants for the Arizona Desert

I just planted six of these on my property and after the last cold night all the leaves on them turned dark, did the cold kill them? what do you recommend I do?

Some areas of the Valley dropped down into the 20's during the cold spell last week. For young, frost tender trees like ficus this can be life-threatening.

For now, do nothing. Don't trim off any of the damaged leaves or branches until next spring. By then you will be able to see which parts are still alive when the trees begin to grow again. With a little luck you'll only have some die back in the branches. If the damage is/was severe they can die back to the soil level and may need to be removed.

To help prevent cold damage you can wrap the trunks loosely with cardboard, burlap or fabric. They even make a tree trunk wrap which is a crinkled paper product sold in rolls at the nursery. It also helps to completely cover the tree with fabric making sure it touches the ground to trap warmer air.

Here's a link to a publication on protecting citrus trees from cold, but it will work for any tree variety.

Good luck.

Here is a link that might be useful: Cold Protectin for Trees