probably head to Rotorua and Taupo area if you go to the North Island
hot pools, geysers, Maori culture, rainbow trout springs, walks through rainforests, farm visits ... stuff that young children like to do and still fun for you
you could also head to where the Hobbit was filmed - they'd probably love the hobbit houses even if they don't know what a hobbit is ...
We took our boys over when they were little .. they loved all that ... there was a luge there also which they loved ... and there's a cable car (we didn't go on that so can't say what the view was like)
There's also the glow worm caves at Waitomo - but be sure that your little ones are ok being in caves in the dark because some just don't like it at all
Queenstown is beautiful and there is plenty to do there - but some of the adventure type activities (jet boats, bungey jumping etc ) they are too little for ... September/early October you might be lucky to still have snow up on the mountains in the South Island. In Queenstown you can go for a day tour on a paddle steamer over to a large sheep property - have lunch, do farm stuff which the littlies just love ... and there's a cable car with spectacular views over Lake Wanaka and the Remarkable Ranges ... you can go panning for gold ... touristy stuff but the boys just loved it all
Don't try to fit in both islands in 2 weeks because although NZ is small in comparison to Australia it packs in a lot in a short distance ... and you don't hit a straight flat road for 200km like you often do here

Plus with littlies they're just not going to love being in the car all the time anyway