No problem. It is possible not to use the word moodle in the address by simply changing the folder currently called moodle to whatever you would like.
For example you can rename www.eagleacademy.com.au/moodle to www.eagleacademy.com.au/main and then access Moodle by going to there. The only thing is that you would have to edit the config.php file (in the renamed folder) so that the wwwroot points to the folder as you renamed it.
You would not be able to have Moodle accessed by going to www.eagleacademy.com.au/onlinelearningcentre unless you renamed your Moodle file to that name (as described above). However, since you most likely have content on www.eagleacademy.com.au/onlinelearningcentre that would get deleted. So you have to think about that.