Question
when is the best time to transplant a small japanese acer

Answer
Deciduous plants may be moved in the spring as soon as the frost is out of the ground, up until the time when new foliage is partly unfurled. In the fall, they may be planted once the leaves start to turn color up until the ground freezes. There being no foliage will help with the possibility of wind burn.

Digging the root ball:

When you want to dig up a tree or shrub for transplanting, retain as much of the root system as possible.  

Deciduous trees  can be successfully moved only if a ball of soil is left around the roots. The exposed roots should be protected with moist burlap or newspaper or with polyethylene sheeting. Every effort should be made to reduce root exposure to wind and sun, keeping the ball as moist as possible. It's best to prepare the hole before digging up the tree you wish to move.

Size of the root ball and size of the hole:

For deciduous trees and shrubs the soil ball should be:

Width = 9-12 in. in diameter/every 1 in. of tree diameter
Depth = 6 in./every 1 in. of tree diameter

For example: A tree trunk 2 inches wide would need a soil ball of 18-24 inches wide and 12 inches deep.

Dig the new hole twice the size of the root ball. Plant the root ball even with the ground surface and fill the hole with good top soil and mulch around the tree with not more than 3 inches of mulch (do not pile the mulch up on the tree trunk)