Mass of earth: 5.972 × 10^24 kg
Launch capacity per year: 15,500 tons
Years to get rid of earth: 385,290,322,580,645,161 years.
I think if we every have to worry about this it becomes more a question of where are we going? And do we have enough carbon to cycle for fuel to do this.
On the other hand if you could capture the Sun's entire output - not just that arriving at Earth - you'd have enough energy to do it in a week or two.
In theory you could simply vaporize the earth with antimatter, converting it to energy, rather than trying to disasemble it. That would produce far more energy than the gravitational binding energy, so unless you happen to have a planet sized lump of antimatter around you'd have to generate it with more than 10^32 joules.
> Is there enough energy to move the entire current human population off-planet?