Moons the size of Earth, orbiting a gas giant, are clearly a possibility. I see no real problem with two Earth-sized planets orbiting each other. the problem I would encounter is proximity of the local Sun for warming, and other radiation requirements. If orbiting a gas giant, there would be a monthly eclipse that could chill the moon to sub-zero temperatures. Also, would the moon be tidally locked, and, if not, are there other Earth-sized moons in the vicinity of this giant? If so, they would be tidally affecting the proposed "Earthlike" moon in ways that would likely make the moon uninhabitable -- for us, that is.

Complicated, to say the least.

Can life exist on such a world? I believe so, but we would be hard-put to live there with any real comfort.

No. An Earthlike planet would be required to have all the things the Earth has, otherwise it just won't work right.

Dan