I think this is a rather heavy choice.
The one thing I’m against is people being afraid of nuclear power, just because its nuclear power. That’s a little irrational there have been thousand of nuclear plants operating in the past 30-40 years and there has only been the odd major accident or two. (Chernobyl, the one recently in japan, 3-mile island, ect). That is not really a huge rate. A lot more people die in coal mining operations every year than the death toll,\ those accidents caused.
Especially in an Australian case; it would be cheapish compared to a lot of the other countries. We would not have to import uranium, since we have bucket loads right here. I think it isn't a good permanent power-source but it is a good stop-gap measure until we come up with something better. If global warming is a legitimate phenomenon and if what they say is true, that we will one day pass a point of no return and it will kind of feed into itself like a loop and then it will be far too late. If these things are true, i really think we need to act now. The government/power companies/corrupt officials/whatever else aren't prepared to accept things like solar and wind full scale just yet.
That said on a global basis Australia contributes relatively little, so just on a local, Australian scale; it is perfectly fine for us to keep burning out coal really. If you mean should everyone, everywhere take up nuclear power that is an entirely different story. The greenhouse gas emissions are a lot lower.
However, just on an Australian scale, i don't really think its worth it. We should go either totally renewable or nothing. The uranium will run out one day too (at least cheap sources). Solar alone is not sufficient as far as I’m aware for power generation though. What about if it suddenly gets cloudy or at nighttime (yes, I’m not stupid i know batteries exist and things like this but still that creates other problems), so it still needs a lot of work. However, i think its either go down the solar/wind road or just keep burning coal cheaply. There isn't much of a middle ground for nuclear.
Another concern with nuclear is the waste, it will be around here for a longgg time. They have some reactors that produce waste that only lasts a couple hundred of years instead of thousands but still that isn't ideal.