Your child does not need any documents to pass through the checkpoint.

Carriers reserve the right to require proof that he is <2 YOA (the cutoff for not requiring an assigned seat). WN is famous for requiring this of everybody, although it seems a little silly at 6 months (unless your kid is enormous).

Frankly, it does always make sense to carry some piece of ID should you ever be asked to it in connection with signing consent forms and the like for medical treatment while traveling. Since you have several such documents, why not simply carry one of them?