Who better to do the job? In fact, with Security Council authorization, Egypt might be the only country that could make a difference in time.
Gaddafi's air force that he has reportedly unleashed on the demonstrators relies on a dozen or so, 1960's vintage Mirage F1s. Egypt has 240, late model American F-16s plus a gaggle of modern Mirage 2000s, more than a match for Gaddafi's older French jets.
On the ground, Egypt fields modern armour including the America M-1 Abrams tank. Gaddafi's forces rely on the antiquated Soviet era T-72 which is pretty much just target practice for the M-1.
Most of Libya's stuff is pretty old including its surface to air missile batteries which are all but useless against modern electronic countermeasures.
Egypt stands at Libya's eastern border, the part of the country that is already under the demonstrators' control. This could be over in an afternoon. The Egyptian air force could easily take out Libyan airfields (runways and bunkers) and demolish the garrisons of those ground forces loyal to Gaddafi. Take out their critical infrastructure including their command and control systems and they're essentially homeless. With no air cover and the prospect of Egyptian M-1 tanks rolling on to Tripoli, Libyan military commanders would be left with a pretty hard decision and I doubt it would go Gaddafi's way. Probably the worst of them would just pack their bags, with or without Muammar.
If external muscle is what it's going to take to pry Gaddafi's claw from Libya's throat it'll have to come from the land of the Pharoahs.