Sounds like a good idea. I would leave the current toilet alone so it
can be used (even if the house ins't currently lived in) and try and
bring the new upstairs stack down by the side of it so that it can be
tapped into once the upstairs is completed. This will obviously need a
new pipe going through the wall for the downstairs toilet and a turn
connecting into the new stack. You might want to check this is all
within code as I'm not a plumber, but have done something similar at my
own house.