I have had this issue at my rentals many times. A new floor raises the
height above the ring. I was told by an ole time plumber to always replace
gaskets, etc. It isn't usually worth the money saved. Used gasket type
fittings can have worn channels in them that don't align with the new.
They can be brittle, or have begun to deteriorate. Use new with new. No
question in my mind on that.
I agree with Keith that you'll probably need longer bolts; wax rings are
sold that have a plastic extension on them to alieviate this problem and
they work very well. You can use more than one wax ring, if you wish, but
be careful that excess wax does not block the flow from the toilet (had
that happen once, ugh!). (When seating the toilet onto the ring the wax
may flow inward toward the open hole, so be careful in placing the toilet
straight down and wiggle a little for a nice seal without gaps.
Good luck. Oh, I usually go to a plumbing supply store. They usually have
everything and not just the most commonly used items that your home
improvement store carries. The counter people are generally friendly and
like to "cabitz". So you can get additional insights.