I actually booked a January sailing less than 72 hours before sailing. However, that was before 9/11, so I'm not sure it would even be allowed now.
There are several considerations. In general, the price goes up as the cruise date approaches. However, off season, this is not always true. Secondly, not only does the ship fill, but each age group fills. Thus, there may be cabins on the ship but no room for a child of a particular age. Again, with school age kids off season, you will probably be ok.
The other thing to keep in mind is that travel seems to be picking up this season (per reports in the Wall Street Journal, etc.) Cruises are tending to book earlier and fuller.
When you book on short notice, you just pick up tickets at the port.