The Internal Revenue Service does not consider personal injury settlements and awards income and, therefore, doesn’t tax them. However, punitive damages are an exception to this rule, as those damages don't pay for expenses and impacts that the child incurred. Punitive damages are taxable. Additionally, if you deduct your child’s medical expenses on your taxes, and then later receive a settlement that included medical expenses, you will likely need to return the amount of the deduction that you took.
Provided the tax code does not overwhelmingly change between now and then, if your child waits until he or she is 18 to pursue compensation for his or her injuries, the same information applies. Compensatory damages (economic and non-economic damages) are not taxable, but punitive damages are taxable.