There are two issues here.

First, SQLite3 accepts UTF-8 and UTF-16, but requires proper methods to be used for inserting data into the database (like using QSQLITE driver or sqlite client library, which is used by QSQLITE too)

Second, sqlite console doesn't support UTF. It may sound crazy but it doesn't do any conversion from what we call a local encoding (like latin1, latin2) to UTF-8 when it passes data to the database. So if you used the sqlite console (sqlite3 application) to enter data, you'll get garbage when reading it using proper methods (meaning, using the client library).

Of course the same stands for reading data from the database. So follow what Jacek has written but also bear in mind to properly access the database, as it may not contain utf-8 characters at all.