No domestic US carriers charge for lap children on domestic itineraries that I am aware of. For some international destinations (Canada comes to mind) the fee is just the taxes. And then for "real" international destinations it is often 10% of the fare, plus taxes and surcharges.

The real key, however, is to know whether airlines base the 10% on full fare or on currently available ticket price. If it is the former there is very little risk in waiting until the very end to ticket the infant. If it is the latter (CO does it this way) it is generally beneficial to ticket as early as possible as tickets should be cheaper.

Another thing to remember is that if you ticket yourself for a reward in the pointy end of the plane you have to pay 10% of that fare, which will likely be LOTS more money for the infant.

And I would not risk the cost of the child fare on hoping to get a nice CSR shortly before departure, especially on airlines where the charge is 10% of the current fare rather than the advance-purchase fare.