They don't commonly take longer, assuming: the infant's photo is acceptable, the application has been properly completed along with the required supporting material, and handled as due from in-person submission and afterward. They often enough get back to the US Embassies/Consulates faster from the US than even straight-forward adult renewals. Domestically-submitted applications aren't exactly the same story, but there is no common issue with new passports for infants taking longer.

I would assume that typically the infant's passport would be back well before your anticipated flight date.