Should a child with COPD have a blood test, to rule out alpha 1 antitrypsin deficiency?

Probably... If a child has copd, and not asthma, then an alpha-1-anti trypsin level probably ought to be checked. The child needs to have an evaluation so the proper diagnosis and treatment can be given!
Yes. COPD is extremely rare in children. Alpha 1 antitrypsin deficiency is a known cause of COPD or emphysema. The onset of lung disease is uncommon before early adulthood. Protein replacement therapy is available to treat this disorder if causing copd/emphysema.