Hi John,
Congratulations on your windfall, must have been an amazing experience!
The investor category certainly seems like your best option, or if you have any business experience you may also be eligible for the Business Visa.
There shouldnt be an issue bringing your dog either. It will need specific injections from a vet, and may have to be quarantined for a while upon arrival, but there's certainly no issue bringing a dog.
If you want to pay a company to deal with all the immigration legwork, our site has teamed up with New Life New Zealand - You can find them by clicking here:
New Zealand Immigration - New Life New Zealand. Their site is mostly geared towards UK migrants, but they also deal with US clients too.