10,843.1 Miles
Once we make it to the moon, let's try for Venus! Mars! The Sun!
Good luck with that. Our solar system is far larger than most people understand. Even the ones that know don't easily understand the immensity of our neighborhood. I presume that you're also going with optimum circumstances with the planets lined up next to one-another, which would make for the shortest possible distances since the planets are normally scattered seemingly randomly about the orbital plane.
Distances from the sun (semi-major axis):
Mercury - 57,909,100 km
Venus - 108,208,930 km
Earth - 149,598,261 km
Mars - 227,939,100 km
Jupiter - 778,547,200 km
Saturn - 1,433,449,370 km
Uranus - 2,876,679,082 km
Neptune - 4,503,443,661 km
Of course, you'd have to do some quick, simple math to figure out the distances from any one of these to any other, like from Earth to Jupiter (778,547,200 - 149,598,261 = 628,948,939 km).
So..., good luck with that, folks!
Meh. Pluto isn't even a planet. It's just a dwarf, like countless other big rocks floating around out there.