If I have 2 tables with the same definition, how would I backup data from it daily? Can I use mySQL Administrator to perform something like this
Yes, you can definitely do that. Have a look at this page: http://dev.mysql.com/doc/refman/5.0/en/batch-mode.html
If you write your script carefully, so that you are not dropping the table and just inserting the new rows you need not worry about losing the data. If you are having a timestamp stored for each row in the table, that makes things a lot easier. You can use the timestamp to load/update the new rows which have been changed or added since the last batch run.
However, its always a best practice to make a backup of the current table before you do the insertion. You can cleanup the backup tables, if the import is successful.