It is necessary to hack Q2A core source. However, because version up of Q2A becomes troublesome, I recommend that you make new plugin with source file below.
File: qa-include/qa-widget-ask-box.php:: allow_template() on L35
1. Case of only question page
Add one line below.
case 'question':
2. Case of all page
Replace function below.
function allow_template($template) {
return true;
}