That's what carry-ons are for. No matter where I fly, I always take the first 24 hours of supplies in carry-ons just in case the AIRLINE delays my luggage. And yes, I did this with two kids, one of them in diapers, arriving late at night and simply not caring when our luggage arrived because we took care of ourselves for the first 24 hours with our carry-ons. I can't imagine NOT packing lots of extra diapers in a carry-on.
And by the way, if the food in question isn't entirely a liquid or gel, then you can bring it in a carry-on. For example, PB&J sandwich, allowed in carry-on. Packets/jars of PB and packets/jar of jelly, NOT allowed in carry-on.