Hi Lani,
I don't have a KK but have travelled a lot with kids and camping. I think that your family would get a lot from the travel and only encourage it. You can travel with less or more depending on your personal choices and finances. The issues I was raising were more to long term travel itself.
Location: are you thinking about a lot of remote area or a mix of urban and rural? This affects a lot of things like access to health care, education, communications, social contact for kids and parents, etc.
Weather: being stuck in a small space in bad weather loses its appeal after a while especially when everything gets damp and wet. Will you have the ability to move location or obtain temporary accomodation such as a cabin?
Education: No doubt travel broadens the mind. My kids have travelled a lot around Australia and overseas. But there are legislative requirements regarding attendance that need to be addressed. Can you home school and do you want to?
Communications: essential for safety but also social contact with family and friends. Maintaining those relationships helps ease the return to a "normal" life.
Other: there are a myriad of other questions to think about, but as I said I am not sure the KK is as big an issue as some of the other questions.
Looking forward to seeing your photos of your great adventure.
Cheers
Shane