If you have the latest full release of VoiceAttack(v1.7), there's a link to the folder which contains the profile database(VoiceAttack.dat) in the options:
Click
, click the "System / Advanced" tab, then click the "Click here to browse VoiceAttack's data folder." link.
You can repeat the process on your new machine and paste the files there.
EDIT: Fixed image links