Nějak takto:

QString path = "path";
QSqlDatabase db = QSqlDatabase::addDatabase("QSQLITE");//not dbConnection
db.setDatabaseName(path);
db.open();
QSqlQuery query;
query.exec("create table person "
          "(id integer primary key, "
          "firstname varchar(20), "
          "lastname varchar(30), "
          "age integer)");

Tady je dokumentace:
https://doc.qt.io/archives/3.3/designer-manual-8.html