" I figured it would be easier to copy it, and then just delete all the records in the new table, rather than build it from scratch."
How do you figure? Creating a new table takes one query, copying and then deleting takes at least two queries. 🙂
Anyway, to copy a table you can literally select it into a new table and mysql will copy the table definition too.
http://www.mysql.com/doc/en/CREATE_TABLE.html
about 3/4 down the page there is this:
If you specify a SELECT after the CREATE statement, MySQL will create new fields for all elements in the SELECT.
Read that part, don't start experimenting right now, read it first!