Question
Can a "white gold dwarf cherry" survive in a location where bedrock is 18 inches below the soil surface? The final height of the tree should be 10-12 feet tall. Does this species have a tap root that needs a deeper soil? A Golden Rain tree (mature) and another 3 year old edible cherry tree are growing nearby in presumably similar soil conditions.

Answer
It should -the root system is generally in the first 18-24 inches of soil. The problem would be during droughts the soil may dry faster since it is not too deep. What I would do is make a small berm and plant the tree on this berm and mulch around the tree with not more than 3 inches deep of organic mulch not piled up on the trunk. I would dig the new planting hole twice the size of the root ball and as deep this would allow the roots an easier route to grow out rather than down.