Hi mywineman,
Welcome to the community!
It is indeed possible to move from QuickBooks Desktop 2006 into QuickBooks online. With there being many versions in between though, the file has to be upgraded step by step.
We do have an in house migration team who would be able to complete the migration for you. If you give our dedicated UK phone support a call on 0808 234 5337 they will be able to arrange this.
Thanks!