If a toy my child was playing with turned out to have lead in it, how long do I need to wait before I can get him tested?

Lead. Anytime. The test detects the amount of lead in the blood.
Depends on form. If your kid gnawed on the object and likely swallowed leaded paint or had other lead exposure you can test immediately and compare another sample later on to see if the level is going up. Xrays can spot leaded paint chips in the intestinal tract and long term exposure can result in changes in blood cells and bones.