whatever works , works
I have literally run hundreds dishwasher like this. 5 to 15 feet away and never a complaint. I have seen it over and over.
very simple , very easy.
Its really not a problem, and you have an outlet on the disposal for the discharge which is why it is there. totally legal.
these units will literally pump quite a ways away from themselves , you are not putting any more head on it, you are not pumping it up to the second floor, so it works perfectly fine that way.
you just drill a hole in the floor under the dishwasher, leave the loop in the line that is attached to the dishwasher on the side of it .
then just drill a hole under the kitchen sink, either you can run it out of 1/2 hard copper, ( I have seen this countless times ) or I myself have run 7-8 raradiator hose up to the flood rim (under the sink) hang it there with a clamp or hanger , and back down to the disposal... connect it to the dishwasher line with a couple of clamps and a piece of hard copper "connecter " inserted deep into the radiatior hose and deep into the dishwaher hose with a clamp tightened down on both.,, and you are good to go.
an interesting side note...
this same radiator ss hose clamp technology is already commonley used in all commercial jet planes ---ect ---think of that the next time you are flying at 35,000 feet in a thunder storm...
If its good enough for a jet plane, with lives on the line, its good enough for grandmas new dishwasher.
But if you do decide to make a project out of this , and run a drain to this dishwasher, a mistake I made one time was to take the high drain loop off the side of the dishwasher and run that down to a drain. DO NOT DO THAT. Some brands out there need that high loop left tied on to the unit or it simply wont fill up the unit peoperly, it just pours down the drain.
its the same with a washing machine. it depends on the brand.
good luck to you whatever you decide to do..