It will take a Rogue planet travelling at 13000 km/sec , about 6000 years on average to travel to nearest , six , Earth- like planets . Or about 36000 years to explore the nearest six Earth- like planets altogether . For an advanced self - sustaining civilization living inside this travelling planet , it is perfectly possible to colonize such planets .
But the mass of a planet means you go in the direction you are travelling in so those six earth like planets need to be in the direction the rogue planet is already heading in and in a line and once you have past those planets they are gone... no going back.
The energy needed to steer and fly this rogue planet would be enormous.
I seem to remember reading a book on ways to potentially destroy the planet and it mentions the energy required to move the earth off its orbit and either directly into the sun or out off into deep space was approximately the same as the energy needed to completely destroy the planet.... and was enormous.
The only way I could think of would be if you could develop gravity wave energy, so you could have gravity stations all around the planet which are directed at local masses which either push or pull depending on where you wanted to go... a bit like Spiderman and his webs flying through a city of high rise buildings using his spider webs to pull him around... except on a much larger scale.
Theoretically gravity waves have no range limit... technically the gravity of galaxies thousands of light years away are exerting a tiny pull on you right now, but the effect is so tiny you can't measure it, which means if you could create a gravity manipulator you could push or pull your way through space... if you think of the traditional way of viewing gravity as the mass being a ball on a springy surface like a trampoline... the greater the mass the deeper the depression and so other mass approaching that mass fall towards it when they get close enough to the distorted or curved space near by.
In that sense a gravity device might curve space ahead of the mass to make it fall that way too... but how much energy it would require to move an entire planet is hard to say...
Even if it would work in the first place.
Note most Sci fi stuff have inertial dampeners so that when their ships accelerate away at the speed of light the crew is not squashed flat like jam on the rear walls of their ship. The only other way around it would be to put everyone suspended in a liquid, but even then they could not accelerate the way they are shown to, but then they would also float around their ships when travelling anywhere.
In Star Trek they often travel at a specific speed like warp factor 3 or something, yet they depict the journey as needing constant engine operation to maintain that speed when in fact once they have achieved the speed they could turn the engines off and would only need to use the engines to change direction, or speed up or slow down.
Their sublight engines would be the same.
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