I originally thought the question was about caulking or some such...
 
This is my sort of question... ;-)  (See Crib and Cradle Safety FAQ
for more info)
 
None of the demonstrably safe finishes (pure tung oil, walnut oil, other
vegetable oils, Behlen's salad bowl finish etc.) are hard enough for high
wear surfaces such as floors, or other fixed wooden surfaces in a home.
None of them are waterproof either.  And most of them take a fair bit
of time to dry.
 
Many ordinary finishes become safe once they've thoroughly dry.  But,
"thoroughly" often means on the order of weeks.  And "safe" is
relative.
 
An ordinary non-exterior polyurethane is likely to be okay.  Exterior
rated polyurethane has more additives.  But I think you'd be prudent to
keep your low-slung pets off it for a week or two.
 
My best advice would be to use one of the new water-based polyurethanes.
These have a number of advantages over the traditional oil/solvent-carrier
resins.  They dry much faster, much less noxious, clean up with water,
are clear rather than amber, and are pretty inert once dry.  By all
accounts, they're superior to oil-based in all respects.  Somewhat
more expensive though.
 
[Posted in FML issue 0664]