So this question is nearly 10 years old, but it popped up on one of my searches, and I think that there are better solutions when programming in Qt: Signals & slots, timers, and finite state machines. The delays that are required can be implemented without sleeping the application in a way that interrupts other functions, and without concurrent programming and without spinning the processor - the Qt application will sleep when there are no events to process.
A hack for this is to have a sequence of timers with their timeout() signal connected to the slot for the event, which then kicks off the second timer. This is nice because it is simple. It's not so nice because it quickly becomes difficult to troubleshoot and maintain if there are logical branches, which there generally will be outside of any toy example.
A better, more flexible option is the State Machine infrastructure within Qt. There you can configure an framework for an arbitrary sequence of events with multiple states and branches. An FSM is much easier to define, expand and maintain over time.