Obviously, it would run out of fuel before too long, but not before you make it to the next solar system to find a replacement planet you can steal.
...or consume for fuel, ala Unicron.
Whatever kind of mobile planet you're envisioning, you're probably leaving the neighborhood of a star behind for extended periods. In which case, you'd either need an appropriate substitute - a few ZPMs, a Green Lantern ring and a wielder with incredible will, some large-scale fusion or anti-matter reactors, or a steady supply of
Powerthirst 
- or a planetary environment and inhabitants that are compatible with being powered down during the journey between stars - like some versions of the backstory for The Transformers have Cybertron doing during most of the millions of years that the Ark lay dormant under the volcano on Earth. (Which provides about the best explanation I've heard for how that long span of time could have passed, and yet Shockwave, Elita One, and other contemporaries of Optimus and Megatron could still be kicking around even though there's a war on.)