We don't really know because to answer this question we would have to know what the Milky Way looked like 5 - 10 billion years ago. We think the answer is that it would NOT look like a quasar, because quasars seem to require the existence of a giant, supermassive black hole containing over 1 billion solar masses of material. The Milky Way has nothing like this in its core, and may not have a central black hole more massive than a few 100,000 times the mass of the Sun. It would not have been able to produce much fireworks. It could, however, have been a Seyfert-like 'starburst' galaxy, with an output of a few percent of a quasar for a few million years.