Why bother with an asteroid? If you're able to get into Earth orbit, just go the rest of the way and slam into the planet. Or do what they did in the B5 spinoff...which I think was called Crusader or something (I don't care enough to Google it) and poison the planet. Sisko was able to cobble something together on the run on the Defiant to poison a Maquis planet, so I'm sure the Breen could do the same to Earth with some planning.
Anyway, as we later hear the Founder promised Earth to the Breen as part of joining the war on the Dominion's side so the Breen are going to be a bit reluctant to blow it up before they even get the keys to the planet.
What was being suggested by the OP was more than just using an asteroids natural mass and velocity to cause an extinction event by changing its trajectory. The Xindi weapon aimed for the complete destruction of the planet, not just extinction, and accelerating an asteroid near the speed of light would achieve that. Of course, infinite energy is required as one approaches the speed of light, making the mass of the asteroid immaterial. Rather than a convoluted scheme to accelerate the asteroid near the speed of light, just direct the energy at the planet. It would do the same job, and probably wouldn't need to be as precise of a weapon.