Sorry for the late reply ChristianZionist, hope you still read this:
New Zealand does have an islamic problem however not to the extent that Australia does solely because New Zealand has a much smaller muslim population than we do. Most muslims in NZ have moved there alot more recently than the muslims here so they haven't been able to create gaza/harlem like ghettos the way they have here just yet. Another advantage that the kiwis have over us is that they are extremely isolated even compared to us so most immigrants in the past have chosen us over NZ due to the distance factor. I also doubt that black styled muslim gangs would want to start causing trouble over there as the Maoris would absolutley destroy them and expose them for the cowards that they are.
The main difference between NZ and Aus however is that we have a relatively right wing government that does to an extent control who comes here whilst NZ's current government is extremely left wing and has opened its borders to any muslim/3rd worlder. NZ's prime minister, Helen Clark is a notorious lefty of the worst kind and hasn't been shy about expressing her anti-Israel sentiments.
I suppose the closest equivalent we have to the BNP is the Australia First Party, who are against pretty much all immigration and are extreme nationalists. I do not know of their particular stance on Jews but I would assume they would be on par with the BNP and other nationalistic groups, that is not particularly affectionate towards Jews. They have made various remarks against muslim immigration in particular, however compared to the BNP in Britain, they are extremely insignificant and most Australians have probably never heard of them. They partially co-ordinated the Cronulla riots of 2005 which gave them a bit of notoriety however.
Another outspoken ex-politican who co-founded the anti-immigration party "One Nation" in the late 90s, Pauline Hanson has stated that she wants all muslim immigration stoped. Hanson however, built her party's platform on anti-Asian immigration which has soured my opinion of her somewhat because Asians unlike muslims are hard-working, educated and productive members of society. She has also stated that Judaism is "un-Australian", revealing her to be an ignoramus. Her party is now dead anyway.
I suppose in the current political spectrum, the only particular parties that hold explicit anti-muslim views are fringe, nationalist parties. However, having said that, the current party in power, the Liberal party (which is the centre-right party despite the name), has placed some provisions on migration and does not adhere to an almost open border policy that the main opposition, the Labor party would surely implement and have implemented in the 80s to the 90s when they were in power. Our Prime Minister, John Howard and our foreign minister, Alexander Downer are absolutley supportive of the United States unlike nearly any other nation on earth, and in my opinion, have a great affection for Australian Jews and Israel. Having met Howard at a few Australian-Jewish functions, I do believe that he realises that the musims are a threat to this nation however, stating so publicly would surely kill his political career, not because the public at large would not agree with him, but because the media and other politicians would destroy him for stating such politically incorrect fact. We do have many leftist morons here but the average Aussie in my opinion knows what Islam has in store for this country, it is just a shame that nationalist, possibly anti-semetic groups are the only ones with explicit anti-muslim immigration policies.