I can empathize with your plight. Logic and common sense would say that you complied with the letter and the spirit of the airline rules when purchasing the ticket. Through no fault of your own, you will be out of compliance with those requirements after the rescheduling of the flight. And, there is no Appreciable difference between an average 23 month old infant and an average 25 month old toddler. There’s even less of a difference between a 729 day old child and a 731 day old child. Logic and common sense would say that the airline should make accommodations for you to be able to hold your daughter.
Unfortunately, in the US, there are also federal regulations with which you must consider and the airline is required to ensure you comply. Title 14 of the Code of Federal Regulations (CFR) Part 91.107(a)(e)(i) States the following:
§91.107 Use of safety belts, shoulder harnesses, and child restraint systems.
(i) Be held by an adult who is occupying an approved seat or berth, provided that the person being held has not reached his or her second birthday and does not occupy or use any restraining device;
The aviation authorities of other countries probably have similar regulations.
Check with the headquarters of the airline. I don’t see how they are obligated to provide a free seat for your child. But, good customer service would dictate that they accommodate or compensate you somehow while staying in compliance with federal regulations. After all, the reschedule of your flight was their fault and not yours.