There is no Economics/Science Degree, only B.Com/Science (you can major in economics in this) at UNSW. In B.Com/Science, you can only get 1 major recognised in the commerce part. Business Statistics is basically the same as econometrics. For the science part, you can get a double major in...
You should definitely do a B.Science (Honours) in mathematics. At USyd, you can still major in economics under the B.Science degree. Agree with Affinity that mathematics/computer science would be ideal for a quant.
You don't have to get a PhD to get a quant job. Here a few examples for Tudor...