Separate Dishwasher Trap and Vent

I will soon embark on installing the plumbing for a dishwasher. The distance of the dishwasher is too far away from the sink to be connected. I am wondering whether the following will work.

Install a separate ptrap and vent pipe to the existing venting system. On the inside of the ptrap, install a dishwasher tailpiece pipe. The separate ptrap would be vented from outside the house.

It can be done, if done properly, but your description is too simplistic for us to tell whether you would be doing it correctly or not.

Thanks for your reply. See the attached for more detail to what I have in mind.