G'day, rotor. I'm sorry that no-one else has taken the time to reply to your questions.
rotor wrote: Fresh Joomla 3.4.3 install
Fresh Kunena 3.0.4 install
Are you sure you mean K 3.0.4 and not K 4.0.3?
rotor wrote: The site is installed in an addon domain and sits in directory TESTSITE under /public_html like all good addon domains must! The addon domains name is say - onetwothree.com.au
The domain name onetwothree.com.au exists, that's true, but there is no website for it.
rotor wrote: So the domain name is not the same name as the addon domain ...
That's not quite correct. The term "add-on" domain relates to your webhosting service. When you purchase a webhost you [typically] receive a the right to host one domain—referred to as your primary domain—and [perhaps] the ability to
add other domains that you may own. These
other domains are usually referred to as add-on domains. As long as you own the right to point the DNS of a domain name to a webserver, you can use any domain name that you like and, yes, you're right, this shouldn't affect the matter.
As long as we are not confusing the terms
add-on domains with
sub-domains (or even "parked" domains) then I have a general understanding of what you're referring to.
I simply don't have enough information from what you've posted to be able to help you here. You have a couple of choices: (a) you can hold out hope that, perhaps, you will get some free advice on this forum that resolves your problem—this could take a while; or (b) you could contact me and we'll see what we can do together.