Hopefully one of our expats in Hanoi gets back to you.
In the meantime, have a look at the Accommodation in Vietnam page for a bit more info, you might also want to have a look at the Cost of Living in Vietnam page.
The average price of an apartment in the city is around AUD 540. So, AUD 350 seems like a faily good deal. I would get photos of the apartment, inside and out, ASAP before making a decision though.
Most expats do live around the West Lake (or Tay Ho) area, so it seems like you're headed in the right direction.
Good luck, and enjoy your experience!