Southwest does require the age verification for a lap child - in your case there is also a requirement that they can't fly babies less than 14 days old without a medical release, so you'll be pushing up against that requirement too. I'm not completely clear if you buy a ticket for the infant normally you wouldn't have to provide ID - only for lap children or child fare - but if you are on the edge of the 14 day limitation you still might need it or the doctor's note. Here's the whole section for your reference: https://www.southwest.com/html/customer-service/family/baby-on-board-pol.html
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