"I'm thinking aabout replacing the carpet in the hallways with laminate

floors or tile to handle high traffic.
Without the carepet and pad, I can tell the the bathroom and and
bedroom
doors will have a large gap underneath.
Is there something made to fill this gap other than replacing all the
doors? "

Some of this depends on what type of floor you have, ie joist
construction with plywood, or slab. If you go to put tile down on a
typical plywood floor, the floor needs to be stiffened by adding
another layer of plywood first. That will take care of your gap. It's
more likely you would have a gap with laminate flooring. However, the
solution to that is the same. You can lay down plywood first to make
up the difference.

In any case, the solution is simple and I wouldn't let that be a big
issue in making a choice. As for which to use, for entrance ways and
high visiblity areas, I would go with the tile. IMO, it adds value to
the house as it looks good and it's the real thing. I would only use
laminate eg Pergo in areas like a basement home office or other less
visible areas. It serves a purpose, but if you look at it, you can
tell before long that it's not real wood.