Based on several theory threads that have been posted here on the Space.com News boards. There's several things that may happen, and one of them, yes, the Earth could even be in the jets of a quasar a few billion years from now.
Start at the beginning, the process of two large galaxies like the Milky Way and Andromeda crashing into each other is pretty much expected and accepted by most. The date of this process is to begin that I remember is in about 200 million years (that may be wrong). And, the process of the two mergers, mingling and orbiting each other until the two central black holes merge into a singular and more massive black hole could take up to two billion years, give or take allot of hundreds of millions of years. But, that would be the beginning of what's needed for a quasar to develope. The massive black hole being just one, after that, it would take several hundreds of millions of years before the 'quasar' stage would begin (gotta give time for the gas/dust/whatever to fall towards the new black hole).
Now, during all that time, there's allot more peril or grace that the Earth could become part of during the dance of the two black holes and galaxies merging. The stringing out process (the first few orbital passes of the galaxies merging) of the two galaxies could either transport the sun and solar sytem out on one of the strings or push the solar system towards the central location of the two blackholes getting closer to each other or keep us somewhere inbetween one of these two extremes.
If we're in one of the strings, generally, nothing traumatic will happen to the solar system, we'll be transported so far away from the dangerous central areas that only if the quasar jets happen to be aligned to our section of the strung out arms of the former galaxies will the solar system get kicked with lethal volumes of radiation.
If we're in the region that is in between the two merging galaxies, odds are the solar system would end up in orbit around the plane of the two merging black holes anywhere from being too close to the central area to the edge of the plane of the new galaxy. Either way, we'd be exposed at some point to too much radiation from the mergings for too long for any life in the solar system to survive, or care where the quasar jets are actually pointed. It would be overkill if we end up as part of the central region of the new galaxie and in an orbit that may have us pass thru the jets of the quasar at that point.
The third location we could end up in is to be inbetween the two orbiting black holes for a long enough time that the solar system would probably get ripped apart and not be recognizeable. In which case, most of the matter of the solar system would actually probably be part of the materials needed to fuel the quasar. The quasar would happen long after the solar system would be shredded.