If you want the boarder protrol TV programs, yes they do ask. Both Oz and k1w1's will ask if they thing you are going there for a longer period (30days+) of time travelling on a tourist visa or just generally look like you probably dont have sufficient funds to pay your way. Tourists doing casual work is a problem in both countries.
I have not been asked but have seen others, including a freind back in the 80's arriving in Sydney
In NZ you are highly unlikely to be asked as you have your wife and child, indicates some level of responsibility, and dont look like your a hippy backpacker, that is going to sing for their supper. Even if you did showing AMEX will generally indicate that you have some level of funds greater than NZ$1000.
Join Australian Frequent Flyer (AFF) for free and unlock insider tips, exclusive deals, and global meetups with 65,000+ frequent flyers.AFF members can also access our Frequent Flyer Training courses, and upgrade to Fast-track your way to expert traveller status and unlock even more exclusive discounts!