Oh God, definitely YANBU. Cannot believe the Travel agent, she sounds like a bloody jobsworth! I went to Cuba with DH and DD when she was 6mth old and that was far easier than travelling to Mexico when she was 13mth old and fully mobile!
Try to find an airline with bassinets (most holiday company airlines don't do them anymore, Thomas Cook certainly don't), but it's not the end of the world if you cannot - we didn't have a bassinet. Do contact the airline though beforehand either way; they have medical seats at the front of the cabin with greater legroom and, assuming someone with a greater need for them doesn't board, usually the airline are happy for you to have those seats.
Other than that, make sure you have a very comprehensive insurance policy, take calpol, ibuprofen, teething stuff and other medication, take sunscreens and mosquito repellent and obviously pack enough nappies, as they can be expensive in resort. I was bf DD, so didn't have formula to pack.
Once you've booked, contact the airline as many give an additional luggage allowance for infants FOC - we got an additional 15kg allowance each time we flew long haul with an infant. Finally, enjoy!