Hi
JAT3 and T3 both are different framework using different features and configurations.
If you are planning to move on JA University based on T3 I suggest you to first install the quickstart package on JA University T3 Here and play with it to know about T3 and its settings.
Here is documentation .
Then you can install your site backup on your staging domain and install T3 plugin, JA University T3 template and all extension comes with it and configure them with help of documentation.
Do not play with your sites. Always take backup of site before any big update.
Regards