Yes, azaleas and rhododendrons are shallow rooted. Also, they can be moved any time, however some times are safer when the plant has less stress. Pruning is recommended to remove the demands on the roots.

When transplanting a large plant several steps should be followed:

First, it is best to stimulate a tight root ball by root pruning the plants to be moved about a year before moving. This is accomplished by cutting a circle around the plant stem with a shovel to cut off roots that extend beyond this point. This radius is usually slightly smaller than half way to the drip line.

Second, it is best to move when the plant is dormant and not stressed. This would be in the spring and fall when the plant is still dormant but the soil is not frozen. Moving in the fall before the ground freezes is preferable if you don't have a problem with frost heaving. Sometimes winter freezing and thawing cycles can actually lift a transplanted plant out of the ground where the roots are then desiccated and the plant dies. For this reason, it is safer to transplant in the spring after the ground thaws in climates where frost heaving is a problem.

Third, take precautions to preserve the integrity of the root ball. Tie the ball together and support is so it doesn't fall apart. The very safest approach is to dig a trench up to 12 inches deep, around the dripline of the plant. Then undercut the plant to form a cone, removing the soil an inch or so at a time, moving all around the plant, until you begin to see that you are removing roots. If possible, then get a square of burlap under the plant. Tilt the plant to one side, put one edge of the burlap close to the center of the plant, wadded up so that only half of it is on the open side of the plant, then rock the plant the other way and pull the burlap through. Tie the corners of the burlap to each other across the plant. Tie the burlap tightly to keep the soil around the plant roots undisturbed. Then lift the plant by the burlap and the bottom, not by its stems.

Finally, pruning the top helps match the demands of the top to the capability of the roots after they are stressed by the move. People have been known to cut the top off wild rhododendrons before moving and the plants have come back with superior shape. This is drastic and not recommended for a plant you don't want to risk loosing. Rhododendrons and azaleas have dormant buds beneath the bark which sprout to form new growth after severe pruning, hence severe pruning which removes 1/3 to 1/2 of leaf area is quite common when transplanting.

Yardmom, I don't know where you live or how harsh your climate might be...a dense fibrous root system and habit of shallow rooting makes rhododendrons and azaleas among the easiest of shrubs to transplant...even large old plants may be moved successfully if they are in reasonably good health and a little care is taken. Digging around the root system a year in advance would be ideal - most of us don't plan that far ahead unless we are constructing a new home and preparing to take our gardens with us.

You can move them any time of year the ground is not frozen or they are not in active growth. The period of active growth is the time when new foliage buds are opening, immediately following bloom.

You can assume the root system extends out as far as the branches reach, but you can take a somewhat smaller root ball safely. Aim for a root ball with a diameter equal to two-thirds the plants height. Cut a circle around the plant, undercut the roots. Lean it to its side and slip a tarp or heavy cardboard under, drag, don't lift and carry, to the new site. If you pick it up, the weight of soil on the roots is going to damage many.

Place the plant in it's already prepared planting hole, water in well during and after planting. Be careful not to plant it any deeper than it was originally growing - if you've reworked a new bed, keep in mind the soil may settle some and allow for that by planting slightly high.

Mulch to keep the roots cool and conserve moisture, and continue to water on a regular basis.

(If you are in a very harsh climate - hot summers, icy winters, observe the same timing as would be recommended for adding new plants to your garden for your transplanting)

I have moved many, the trick is to keep them well watered the first summer after moving. I've lost some because DH didn't water when I was gone on business in August.