Qatar has jets?
The Mirage 2000 is a very, very nice interceptor, very comprable to the F-16Is I flew, air-to-air. The sustained turning rate on the Mirage is a bit slower, but it is (at least initially) faster.
Head-to-head, it would depend on the pilot and the weapons and senor platform -— both of which Israel has and had a considerable edge.
Regarding the topic at hand, Lybia:
The Mirage 2000 has crappy fuel capacity and crappy ordinance ability. Or rather, it can carry that stuff, but becomes a flying brick that I could take out with a Purim-sized hang over.
So, don’t expect much from the 2000s.