There are two* classes of SQL commands:
DML: Data Manipulation Language is a set of commands that allows you to query and manipulate the data in your database.
DDL: Data Definition Language is a set of commands that allows to you manipulate the structure of your database: add tables, manipulate indices, etc.
Qt unfortunately only provides any level of support for the first, not for the second. It is possible to add this, but it is complicated. I wrote an extended set of Qt database drivers for MySql and for MS Access once that adds these features, as I used them a lot. These drivers added a lot of options to QSqlDriver::sqlStatement, as well as some other features. If you're interested: the code is available under GPL.