I have moved on to Amazon AWS from Google App engine. I manage my own cloud server and it has scalable options if needed.
There are many restrictions to the Google App engine-PHP such as uploading files (u have to use Google Cloud Storage), SQL configuration is cumbersome, certain APIs are blocks such as curl, etc.
I could not get Google Cloud Storage to work to upload images and that was my breaking point.
May be recently GAE has changed the restriction on API but still I find much better to manage my own server.
If you still want to install the Q2A on GAE then follow the procedure to install the wordpress on GAE. It is very similar.