Personally (and again, my experience of doing this has generally been with airlines that are somehow affiliated), I would not try to do OLCI check-in for either AMS-FCO or FCO-DOH-KUL in advance (as once you've done OLCI, a check-in agent may then claim they can't make any more changes). And I wouldn't try to approach the QR check-in desk in AMS. Ideally I would go straight to the KL check-in desk, present both tickets, and ask them to link the PNRs (or whatever it is that they need to do), so they can therefore check bags all the way through, and ideally issue boarding cards all the way through.

Unfortunately however, you probably can't "go straight to the KL check-in desk" in AMS, as they will try to force you to do self-service check-in first (even though there's no way that self-service check-in would let you add on the QR flights). So, I would probably go to the KL ticket desk first (at the left-hand side of the main KL check-in area), explain the situation, and ask them to link the PNRs (I think they can even print boarding cards, although you'd still need to go to the actual check-in desk to drop off bags).

If for any reason KL can't check you in for the QR flights, I would then try to find an internet connection somewhere at AMS (having checked in for KL), and do OLCI check-in for QR at that point.

Or, ideally, talk to KL (or QR) in advance, to see how this is likely to be handled. (ie: can they do through check-in from AMS, and what are the implications if the KL flight into FCO is more than 2 hours late...?)