How does the red gum we have here burn compared to the varieties you have back there or are they all about the same
Good question, not sure I can answer exactly. There are a few variants of red gum here and they're close to each other in how they burn and how heavy they are. Red gum here sits between black locust and hedge on the BTU charts and is about in the middle for Oz eucalypt species for density. But I've read that when planted outside Australia the density is lower for some eucalypt species so it may not be as good over there. Then again, if you have a fence line of them rather than a close planted plantation it may be more like it is here.
Red gum is what most people will buy for firewood in my neck of the woods and it is well regarded for burn time and low ash content (apart from the bark) though there is better wood a bit further inland and north of here.