basically with a good set of allen keys, you have 3, but you may need a few more sizes and a bottom bracket tool, you should be able to do this. being 600 groupset, I'd bet its an octalink BB so basic BB tool is all you should need, probably $20 would get you that one from and LBS or a chain store and a full set of allen keys from Repco or Bunnings will be up to $30 depending on quality.
in terms of swapping the gear over, its really quite simple, the only issue you will probably run into is cables, specifically the outers, you may get lucky with keeping the inners only. but to be honest, I'd replace both, either way $50 will easily cover new inners and outers with lots of change I'd hope.
if you need a hand and want to use my tools, you're welcome to come over. that way you know the tools are all available and you then know what tools to go an buy for next time.
