Are you sure the display module you describe does not have an integrated display controller? The pin count seems low.
You can drive a QVGA with almost any MCU as long as the device has enough I/O for the task, like the project tpetar mentions above.
However, if you want to accomplish the task in a reasonable time frame and still have resources for other tasks, I would strongly recommend an ARM, PIC32 or device with similar resources.
I have successfully used a QVGA with a NXP LPC1768 in a commercial project.
If you need a device with a dedicated display controller for better throughput, the NXP LPC1788 is one such MCU which could meet your requirements:
**broken link removed**
Some other devices from the NXP ARM family with integerated display controllers are:
LPC1850, LPC247X, LPC325X and LPC4300.
Of course there are other devices available from numerous manufactures, the LPC family just happens to be the family I'm most familiar.
BigDog