It's not entirely implausible for two earth like planets to form this way, The giant impact hypothisis is after all almost exactly what you described. The one limiting fact that I see is that were one of the two bodies to end up with most of the iron (and by extension nickel) then the planet may not be able to generate a magnetic field. The movement of the molten metal core forms a geodynamo that produces the magnetic field which protects the atmosphere from the solar wind. Without the magnetic field, the solar wind will strip the atmosphere from a planet. So if the world with the small iron core did develop earth like conditions they may not last long.
All other things being equal, the planet lacking the large iron core will also have a lower mass and by extension gravity than the other. Earth's core is about 1/3 of the mass of the planet. While not that big of an issue it does pose problems for gaining and holding onto the atmosphere especially when being blasted by the solar wind.
As for their orbit, they would orbit like the earth-moon system. This means they orbit a Barycenter, the center of the masses of the two planets. For the earth-moon system that point is beneath the crust of the earth so from a distance the moon orbits the earth while the planet wobbles. Given the likely dissimilar masses the orbits may look like the pluto system:
In summary, the system is not unrealistic. The two planets would have large differences in their masses and one would likely have a thinner atmosphere. But they could have earth like conditions and evolve life.