Let's understand QR "legal" logic.
First, the infant ticket. You booked two separate tickets. Only the first ticket is affected. Because of the downgrade QR should refund you the difference between BKK-DOH F and J on that ticket, although fares might have changed. You are asking for a refund that most/all airlines would not entertain: asking to merge the two tickets into one (lower fare) and then get the difference between 2 tickets F+J and a single ticket all in J. This is frustrating but your only option is to get both tickets refunded and buy a new one BKK-IST, that will be cheaper. WHile QR should not impose a penalty for the first one, they certainly will for the refund of the second one (depends on the fare rules)..
Second, your avios redemption(I assume you have a QR Privilege account that you used.) It seems that this was booked as a single ticket with mixed cabins (not separate ticket). As your flight is not cancelled, QR cannot change your flight without reissuing the ticket, and there is no more avios availability on the DOH-IST segment of your ticket. With some airlines, a supervisor might have the authority to override the system and let you fly on the earlier BKK-DOH flight. But QR employees play by the system and are usually not entitled to override it unless you go very high up. Still, they should offer you some avios for the downgrade of the first segment. But we have seen examples where F was as cheap as J on married segments.
Your case is complex because of two separate issues (you and your infant). I suggest following KingCanute suggestion and hold some hope for a small partial refund or a complimentary change to the earlier flight if availability.
BTW: I do not know when you are travelling, but the aircraft for the flights BKK-DOH could change, same for DOh-Istambul.