We are having a toilet relocated to the other side of the bathroom. There will be a 6 foot run of waste pipe under the floor, that will connect to the stack that currently exists. The new toilet we are buying is a 1.28 GPF low-flow toilet.

My question…will 1.28 GPF be enough water to remove the waste along the 6 foot pipe, or will it sit in the pipe. Are we asking for trouble with this configuration?

Besides that question have you considered the floor joist arraingment,(you can't be cutting floor joists to move it) and can you have the required slope to the pipe... they never run level and always need to slope downhill or you will have problems no matter what toilet you use.. Meaning bu extending the pipe with the required slope.. will it put the flange above floor level?

To answer your question about low flush toilets, High-efficiency toilets use even less water than standard low-flow models, some as little as 1.1 gallons. Dual-flush toilets, which have separate flush modes for solid and liquid waste, are another water-saving option. The differences in performance may seem trivial, but switching from a standard to a low-flow toilet can save thousands of gallons of water per year.
Replacing an old toilet with a low-flow model is a simple and fairly inexpensive way of conserving resources—a cornerstone of green building.
Smoothy brings up a good question, Are the floor joists so you can install the drain line without cutting the joists? And I have a few questions. How will the toilet be vented? Let me show you a typical installation using only one vent, Good luck, Tom