Wearing a burqa should not be banned; however, I also don't think it should be required. There is, as has been discussed, a religious freedom to wearing whatever falls within the bounds of public decency and still follows religious teaching. That's a personal choice. From a public safety standpoint, asking that faces be uncovered for identification documents such as drivers' licenses is not unreasonable. I don't consider myself to be a raging feminist in any way, but I do find it rather offensive that only women are required to be so restricted. If it's a choice, though, it's certainly okay by me.
Of course, this is a matter of opinion. I would take the perspective that the burqa is a religious garment, even though in the West it is viewed as restrictive or extreme. As a religious garment, I do not believe that democracies should seek to place limits or restrictions on women wearing them. Nuns and Priests wear robes and habits, which can also be used to conceal dangerous weapons or bombs. Of course, I've never heard of an instance where that happened, but I also have not heard of many suicide attacks by women in burqas in Australia either.
Is the threat real or imagined? Will restrictions be applied to only the burqa and not other types of similar garments and robes worn by non-Muslims? There are many religious beliefs and practices I do not agree with, and I'm sure the burqa is not common or popular in Australia. I don't think that means it should be banned.
The only valid reason I can see to ban this type of clothing is security. I do not think it is wrong to ban people from wearing clothing that covers their faces (like masks). However, I would think that you would need to have at least a few crimes committed by people wearing them before there would be any compelling reason to ban them -- I don't think that the mere possibility that someone would commit a crime while wearing a burqa is a good reason to ban them.
As far as other reasons go, I think they are not valid. It is hard for outsiders to say what constitutes infringements on women's rights and what does not. The Catholic Church does not allow women to be priests and it officially forbids contraception. To me, these are intolerable affronts to women, but my mom (Catholic) does not think so. So who is to say if wearing a burqa takes away from a woman's dignity in an intolerable way.
When it comes to fitting in to your new society, how far does that go? Can you require Muslims (or Jews) to eat pork because most other people do? Can you require Muslims or Mormons to drink beer? I'm not convinced that that is a good reason to tell people how to dress. I would hate to be a woman travelling in one of the UAE, for example, and be told to wear certain clothes to fit in. So why make women do that in a free and secular country?
The practice of burqa, or any similar practice which makes it obligatory for women to cover themselves so completely, while putting no such restriction on men is definitely a case of gender discrimination. I believe such practice should be discontinued in all parts of the world.
What I am supporting is the removal of compulsion for women to wear burqa, or for women in some old fashioned Hindu families in India to cover their faces with veils. This is not same as banning burqa. A blanket ban on burqa will perhaps be as unjustified for women used to wearing burqa, as the compelling women to wear burqa against their wishes.
Perhaps what needs to be done is to change the thinking in the society so that it will no longer insist on women wearing burqa.
Of course, where wearing of burqa creates security risks or interferes with effectiveness of person at work, some restriction on wearing of burqa, or any other practice associated with religious beliefs are fully justified. For example, Sikh religion requires its followers to carry a dagger (kripan) with them in public. However this cannot be an excuse for demanding that Sikh passengers be allowed to carry daggers on commercial airplane flights.