There is no built in backup method for versions before the System Platform series. Well, at least for InTouch 9.5 and before.
So your application directory files are the backup. Just use them. When you startup a new version of InTouch it will convert the files to the newer version.
However, I recall reading that you might not be able to convert directly to version 10, but to version 8 or 9 first. Give it a go and see.
You will have to copy you I/O driver configuration files, if you can use the same driver in InTouch 10.1, otherwise you'll have to use the new driver and do the configuration.
I'm sure someone else will jump in and correct me or add more if I'm mistake. I've not used 6.0, only 5.6 on WIN98 and then we switched to 7.1 on NT (and later 7.11 on XP) and then 9/9.5 so my reply is based on believing that 6.0 is just an earlyer version of 7.x and not radically different in file usage. I could be wrong.