Not necessarily many doctors I work with would not automatically treat, first of all you can have the tick tested for Borrelia, Ehrlichia, Babesia, etc If it is negative, then antibiotics are unnecessary. If symptoms develop (bulls eye rash, headache, extreme fatigue, still neck, and sometimes fever) then treat with amoxicyllin. You did not mention how young. Is the child able to communicate that they have headache or a stiff neck ? It is more tricky if a child to preverbal and not able to say how they feel. Abrogated treatment with 3 days of antibiotics after a bite is not that much better than no treatment according to studies.