There are a few ways you can do this. If your Android app is only for you or a small group of people, you could connect directly to the MySQL database on your server using the QSql library.
However, that won't scale well and it isn't best practice to have direct database connection on an open network.
An alternative way is to use HTTP Post commands to your server where a php script will be able to unpack the information contained within the POST data. Once the PHP script has unpacked the information it can then insert it into the MySQL database on the same server or a different one.
It would be advisable to encrypt the data before sending from your app and decrypting the data in you php script, especially if commercially or personally sensitive data is being transferred.
The following stack overflow questions may help you with creating HTTP POSTs:
How can I create a HTTP POST request with Qt 4.6.1?
Qt Simple Post Request