I suspect this is going to be dependent on the individual airlines' rules. I only have access to CX's which state:
Code:
As it is a flight safety ruling that passengers aged 24 months and above
must be assigned a passenger seat when travelling on Cathay Pacific, with
effective from 04APR05, Cathay Pacific's infant fare policy will be revised
as follows:
Passengers under 24 months of age:
* Not occupying seat: Applicable infant fare will apply
* Occupying seat: Applicable child fare will apply
Passengers, aged 2 to under 12 years of age, must be assigned to a passenger
seat.
Applicable child fare will apply.
The age of the passenger will be calculated at the time of travel. Passenger,
aged 2 to 12 years old, will be required to purchase seat at child fare even
if the ticket was purchased before the child turns 24 months of age.
So if the travel after September involves CX the child will need a child-fare ticket (75% of full fare). I suspect that other airlines will be the same, so the parents will have to work out whether buying a child OWE for the whole journey or seprate tickets for the parts after it turns 2 will be cheaper. I guess probably the former.