Can my child slide head first?

Not while advancing. In the Major Division and below, a runner who slides head first into the base they're advancing to is out, and the ball stays live (Rule 7.08(a)(4)). Diving head first back to a base is allowed.

There's no "must slide" rule, but a runner is out if they don't try to avoid a collision with a fielder who has the ball and is waiting to make the tag.