What? Seriously? I thought for certain it takes two pops to get to ocean terrain just outside the initial borders...well, that sucks. Seems God-emperor was right about koas being farther off than I thought. Well, the other civs will definitely all have archers by the time you get them, but they are still the best city attacking units you'll get for a long, long time.
Just keep spamming the culture buildings in Adelaide. Perhaps even tell them to build culture.
I suspect the reef between the city and the fish slows the spread even more, but I'm not sure. I had expected the 2nd expansion to get it, but am not very surprised it didn't.
At this point (well, OK - too late since this is an episode behind), if you want to wage war I might suggest getting a horse breeder (and stable) built (they can be in Melbourne, at least), so you can build a few horsemen, and research copper working. Javelineers are enabled there and for attacking archers in cities they should be almost as good as a Koa, and better at it if the archer is not in a city:
Javelineer: strength 5, +50% vs. archery units => effectively 7.5
Koa: strength 7, +20% city attack => effectively 8.4 if archer is in a city, 7 if not
They are also a little cheaper (base costs from XML, these are modified by the game
settings but will be proportionately the same):
Javelineer: 35 with a +15% production bonus from cooper (and iron too, which is irrelevant at this stage)
Koa: 40
You can also upgrade an atl-atl to a javelineer, should you have any laying around (I don't think you can build them after javelins become available to you since they upgrade to archers or javelineers and you'd have both; it would be possible to build some before the copper working is researched specifically for the purposes of upgrading them, allowing you to essentially convert some of the gold stockpile to production).
Javelineers are almost as good vs. mounted units as they get a +25% for that, so 6.25 vs. the koa's 7.
On the other hand, javelineers are not anywhere near as good vs. melee units since the koa starts with a free Shock promotion for +20% vs. melee making them the same 8.4 for that too (and even higher if the melee unit is in a city as the +20% for that is cumulative), which is much better than the javelineer's 5 for this. Note that a koa will tend to slaughter a javelineer because both of them count as melee units so it is 8.4 vs. 5 in favor of the koa.
Then once you do finally get some koas made, you can back them up with the javelineers and horsemen (and hopefully a couple battering rams and the occasional archer).
Anyhow, that would be my advice for going on a rampage the moment you discovered that the 2nd border pop wouldn't get you the koas.
By the way, I don't know if you are aware of this but you could be considered to be in a race to get the koas. The Maori are, not too surprisingly, also an Oceanian culture (in the real world they are Polynesian, after all) and can therefore also get the culture that enables the koa (the Polynesian culture). If the Maori get fish before you do, they can get that culture and, since it is a world wonder, that will block you from getting it (unless, perhaps, you can take it from them - but that could be hard if they build koas). Their city north of Perth has a fish somewhere near it, but it is also an ocean fish, not coastal, as I recall. There is no good way of knowing if they have any other cities that have, or could have before you do, access to fish.
Another user interface suggestion: Open the foreign advisor so you (and we) can see who is at war. It should be in the group of round buttons to the upper right, about the 4th from the left, I think. This is the same advisor screen where you can see an overview of resource trading on one of the tabs, and some other stuff. The first tab on that advisor screen shows color coded lines connecting the civilizations that know each other, and from that you can tell who is at war. There have been some war declaration announcements scroll by in the messages and some peace announcements as well. At this point, I have no idea who is at war with whom and I bet you don't know either. It occurred to me after my last post that perhaps the Egyptians are already at war with someone (or could have being in the past, which wouldn't show up there via the color coding but can be determined by diplomacy modifiers between them and the other civs; that is most easily seen on the "glance" tab where you can go across a row or down a column and see what the diplomatic modifiers between civ A and civ B are via the pop-up for each item in the table).
Yet another user interface note: You can see the history of the message that have scrolled past in the upper center of the screen via the messages dialog. The uppermost left button (below the civilopedia button) should be the one. Alternatively you can get to it via Ctrl-Tab. Some messages "decay", disappearing from the log (I think combat messages only last 1 turn - there may be some others that disappear that quickly and there might be some that go away but take a couple more turns to do so). When you wondered what building the fire event wiped out in your capital you started reading the messages that were scrolling past. A few messages after you stopped reading them, there was one that said what it was (the fire dance building, I think). If you had opened the message log, you could have seen it. All the messages go to the log without delay, unlike the ones that scroll up the screen which have something like a 3 second delay between them. This log also has 2 more tabs, one which gives the detailed reports for each combat and another that shows what quests, if any, you have received that you have not completed and which have not expired (you haven't got any yet - there may not be any in the prehistoric era and I don't think there are very many you can get in the ancient era either; they are a type of random event that gives you the opportunity to get some bonus if you do something before it expires or before someone else who has gotten the same quest, which rarely happens, does it).