You don't have to be a permeant residence, tourist on legal visa is enough to qualify as legal resident.... It;s online and they will ask for proof of current location in some cases like a selfie with a newspaper, at very least you should apply on Vietnam Wi-Fi.
I only do workcation so can't help on that but one week is not accurate and the soft power gym or visa agent should prepare all the documents for you, you only need to worry about money in the bank.
One of my DTV clients had a similar problem in Vietnam, they wanted him to produce the person who made the money deposit in his account (his deposit was only recent). It seems to me they don't believe you have the money and don;t believe you are in Vietnam .... Make a cover letter explaining where the money is from with bank statement attached of that deposit and include any other documentation you have that can support that.
Usually they ask for proof of residence before / during application if you already applied without doing that and wasn't using an Australian VPN it's highly likely they are going to refuse or ask for the above... If they do I might be able to help as I've done similar for a Canadian client but no experience with AU embassy.