Cannot Use Backup DB Utility after Host Tranfer

[DrByte]

... I would recommend using the -h command after the mysql dump. You should then be able to just reference the sql host and database credentials to perform the dump.."

The addon already operates that way.
The problem is more likely that the mysqldump binary doesn't exist on *your* server, or (and this is very common) the client isn't kept up-to-date since few people use command-line tools on a server other than the one the database is actually on.