"Non-NATO members participating in the operation would have a seat and a voice, on the model of the operation in Afghanistan, where some 20 other nations participate in the NATO-led war." NYTA seat and a voice, but a vote? Hmmm. In the course of our research on NATO and Afghanistan, I did happen to sojourn to Australia and New Zealand to see what the NATO life is like for non-members (yes, I have a cool job and a really cool research question). What did they say about their role in NATO decision-making? They are treated like kids at the various meetings--to be seen and not heard (at least, that is how the Aussies viewed the French attitude towards them), and perhaps sitting at the kids' table. This was/is the case in ISAF--the NATO-led effort in Afghanistan--even though Australia has more troops on the ground than all but a nine or so members (which means that 19 members of NATO or so contribute less). Which means that Greece, which has contributed only a handful of troops has a vote whereas Australia as a voice only.
Even many NATO members do not really drive decisions. One of my favorite memories from the year in the Pentagon was organizing the QUINT meeting--where generals from the US, UK, France, Germany and Italy were meeting to set the agenda for the next year or so of the NATO missions in Bosnia and Kosovo. No doubt that this new mission in Libya will be driven by those who contribute the most--France, Britain, the US and perhaps Italy since many of the planes are based there. Turkey may have a heap of influence since they would be the ones most likely to block further decisions at the North Atlantic Council.
The punchline--neither Qatar nor the UAE will be driving the bus.
PS Handy tip--keep track of the number of sorties (each individual plane flying a mission related to the campaign--bombers, fighters, early warning, coordinators, refuelers). As long as the number is near or over 100, the concept of the Americans turning the mission over to the Europeans is much more symbolic than not.