Think you have missed the point of the new airline. Contrary to what the Qantas pilots union etc says it is not being set-up to do Australians and existing Qantas employees in general out of jobs, it is being set-up to exploit new markets because there is stuff all growth left in the premium market in Australia but heaps in Asia, China in particular. Of Qantas will feed into this airline, but it's main purpose will be to serve Asia. When it comes to the Qantas name the brand is symbolic of Australia, so would be meaningless to a Chinese person flying to Singapore, so it makes perfect sense to have a different name, but yes it will be hard to start a new brand.
You raise an interesting point about the company name and it not being used on the new airline, but to me this highlights that maybe now is the time to change the name of the registered company so that it that bears no resemblance to any of the brands it owns, including Qantas. So yes keep the Qantas brand, keep the Jetstar brand etc, but change the company name to something that better reflects what the company is about in 2011. Maybe then people would realise that Qantas the company is more than an airline named Qantas, rather it is a group of companies all feeding money into a company called Qantas Airways Limited.
This is very common in the airline industry. For example what is the name of the company that owns the airlines Cathay Pacific, Dragonair and Air Hong Kong? Will give you a hint, it isn't Cathay Pacific.