I suspect you want to replace $1 in your script example with /backup/backup.tar. So it would read:-
mv /backup/backup.tar /backup/backup.tar.$dt
In scripts, $1 means the first parameter passed to the script. Also, I prefer the $() syntax rather than using the back quoted syntax. It makes it less confusing when reading the script with odd fonts. So, dt=$(date +%y%m%d) will still put the correct value into $dt.
Anyway, see how that goes.