Wrong DOB on passport, flying next week...is this a problem?
 

We are US citizens who live abroad. We are flying to the US next week for a visit. We got a new passport for one of our children (4 years) at the local US embassy, but I was dumb enough not to review it. Upon inspection today for uploading documents to UA I saw that the DOB is wrong. It should be September 1 and it is listed as January 9 (one of those US vs European formatting issues 09/01 vs 01/09).
I reached out to the embassy but they seemed not really care. I should have heard back from them by now, but surprise surprise, I have not.
We have a US birth certificate and her old passport on hand to verify her birth date.
I have not reached out to UA yet, out of fear of opening Pandora's box.
I have a few ideas
1. Fly with a mismatch between the passport and the information on UA. Bring all documentation.
2. Reach out to UA, explain the situation and ask for advice.
3. Login to UA and change her DOB in the profile to match the passport, and then fly.

Please provide your thoughts and suggestions.

details on the ticket needs to be same as in passport. Therefore number 3 will be safest I think.. nobodys gonna know nor care what date was the children DOB anyway..

Does the child have his/her own FF account with UA (or a Star Alliance partner) with the FF number attached to the reservation? If so, I would guess that changing the birthdate could raise alarms in the computer system.

IIRC you can't make (some?) changes to secure flight once it's within 72 hours of scheduled departure.

Bring full documentation to the airport. It can be rectified at check-in.