I am writing a program using the Qt framework. I would like the user to be able to have access to a console/terminal from within the application itself.
In other words,
You could try QProcess. This is not strictly "embedding" a terminal in your app, but it it really easy to use, you can kick off a terminal that is owned by your app. You can even connect (with signals / slots) to its output and interact with it in a limited fashion... depends on what you need.
Here is the doc with some simple examples: http://qt-project.org/doc/qt-5/QProcess.html
I am not at my Qt-PC today so I don't have an "interacting" example for you, but if you think this is a way for you to go then I can dig that out...