Hi Will,
If your system has only been up for a week then I doubt it would have cycled; the process where the good bacteria colonise and start doing the work we need them for.
Although it is possible to introduce fish into a system before it has cycled, it causes undue stress on you and the fish, and if you get it wrong then you will suffer ($$$) and the fish will die. Getting barramundi at the moment is hard enough, let alone having to source them twice!
Do a quick search of the forum looking for fishless cycling, humonnia etc.
Having being through the trauma of cycling with fishes (sounds like a Kevin Costner movie title

) I would recommend you investigate the benefits of fishless cycling as the preferred method. Anyway, I still don't think we yet have the temperatures to comfortably host barramundi without resorting to exotic forms of water heating?
I went nearly two years on small systems without having a test kit, and made it... but only be the smallest margin; more good luck than good management. A test kit will give you a good indication about what is going on in the system, especially if there are no other references like plants and fish. The test kit will also allow you to forecast changes before they become catastrophic for the fish and plants you will introduce later. Again, a search of the forum for cycling will give you all the information about how to determine when your system has cycled and when it might be appropriate (safe?) to add fish. In addition to the test kit, a good thermometer will be invaluable to you.
There is also heaps of info here (somewhere) on keeping barramundi in the Perth metro area.
Patience... give the system some time to establish itself.
Scott