If the answer is infinite time, then is there something greater than infinity such that something can traverse infinity in 0 seconds or less than 1 second?
This is not a very well-defined question. Essentially, you are asking to compare two infinities, that is, to find their ratio: inf/inf.
In general, the answer -- well known to mathematicians -- is to examine the processes that caused you arrive at infinity -- to examine the limit:
lim (x -> inf, y -> inf) x/y = ?
Without further specifying what kind of infinities these are, that is, how you got to them, inf/inf is an undefinable quantity.
p.s. can anybody get math rendering to work?
Suppose you were at the start of a road that went on for an infinite number of miles. If you are travelling infinitely many miles per hour (but only per hour!), it will take you an hour to reach the end of the road. Generally, however long it takes you to travel an infinite number of miles, is how long it will take you to get to the end of the road.
To answer your question about something "greater than infinity," let us compare two roads, one ℵ0-miles-long and another ℵ1-miles-long. Since ω×ω and ωω (for example) are less than ω1, infinitely so, if you are travelling at ℵ0 miles per hour, even after ω hours you will not reach the end of the second road. Now, if your speed multiplied your distance per hour, that is if you travelled at some rate that mapped into ℵ0ℵ0, then after ω hours, you would at least reach the end of the second road, if not an even longer one.
(Actually, I'm not sure the above is worded correctly, or if it even can be worded correctly. The best I can say is that something like the above would have to be true, if your question is to have an interesting answer.)