Not sure if this is the right place to ask this question:

I am traveling in J from RIO-PTY-BOG with an infant using Singapore Krislfyer award ticket in Dec. I am trying to book an infant ticket by paying 10% cash for an infant and I am being thrown back and forth between Singapore airlines (issuing carrier for adults) and Copa (operating flights). Finally someone told me the price but I need to pay it at the airport or sales office (none close to 100 miles to my home) and I need to pay the fare within 24 hours of reserving the ticket over the phone. I am worried about the price increasing before our trip and being J, it will be substancial damage if I do it at the airport just before flying. Any pointers?