Opera treats two things separately: the default search engine dropdown, and custom keyword-based search engines you create yourself.

1. Open Opera and go to Settings.
2. Under Search engine, check whether Queye already appears in the default dropdown.
3. If it does, select it.
4. If it does not, open Queye, right-click the search field, and choose Create Search Engine....
5. Give it a name and a short keyword such as qy, then save it.

In some Opera versions, a custom search engine is available as a keyword search rather than as the browser's main default search provider. If needed, search with Queye by typing qy, then a space, then your search term.