Hey Linda,
Here is a website that does a very thorough job explaining what a QEEG is and does.
http://www.qeeg.com/qeegfact.html
Please refer to it for more detailed information. Basically, a QEEG is an electrical map of the brain. Our brains are biochemical and bioelectrical organs. It operates the same way your television or computer does, by moving electrons around in order to "do its job." When this happens, an electrical signal is given off. This signal is otherwise known as 'brain waves.' Different speeds of brain waves correspond to different states of mind. The signals are measured in Hertz and grouped together for easy classification. For more on this, please refer to the website.
What the QEEG does is measure a persons brainwaves from 1 - 40 Hz. It is doing this to ascertain what frequencies are dominant in what area of the brain. A healthy brain shouldn't have any dominant frequencies which would allow for easy flow between different mental states. A person who has a dominant frequency, in your daughter's case it is probably 1-5 Hz and 20-30 Hz, is stuck in these corresponding states of mind. The QEEG also measure coherence and phase relationships. This is basically measuring how well the brain is communicating with itself.
The reason why I suggested getting a QEEG instead of a SPECT scan is because QEEG's are a fraction of the price that SPECT scans are. I believe that SPECT scans cost around $3000 and QEEG's cost around $500. Like I said earlier, they basically tell you the same thing because the brainwave frequencies usually correlate to blood flow. However, one of the advantages of a SPECT scan is that it does give you a 3D image whereas the QEEG is only a 2D image of the brain.
Now, why would you get a QEEG done? Basically for two reasons. The first is for litigation purposes. If you are trying to get SS disability or if you are involved in a lawsuit as a result of the brain injury because this will provide evidence that an injury has taken place. The second reason would be to do neurofeedback to train out the dominant frequencies and incoherences. Of course, someone could get one just for the sake of knowing what is wrong with them.
So, that is pretty much it in a nutshell. Hope it helps.