Is it too late to transplant a rather small (1 year in present location)desert willow to another location

Do it right away or wait until next fall.

These are such lovely trees!

I transplanted back in March as suggested, and the tree is doing fine, but had no blooms. You think it will bloom next year

First year in a new place, a tree is pretty much at 'station keeping' as far as growth above ground and blooms. Much more will be going on below the surface as it takes hold in its new spot.

It'll do more next year, and more the year following.