I answered a similar question recently, which was, in essence, "Was there a peerage system in the British colonies?"

You can read the answer here.

If you read through that answer, you'll see that there were some steps toward a peerage system in some of the North American colonies.

But this never went very far for two reasons:

1. Large tracts of land were bought by (or given to) British peers back in the homeland. The lords back in Britain were more interested in buying North American land for themselves than they were in elevating the status of North American landholders who weren't already lords.

2. The peerage that was on offer in the North American British colonies was controversial locally, and led to violence in the years before the American Revolution broke out.

As for why there were governors instead of dukes, that's because the colonies actually were run by nobility back in England, who would then appoint a governor to do all the day to day stuff. Many of the early governors were peered Englishmen themselves, or else military men.

In New York, for instance, the head of the colony was the Duke of York who appointed Baron John Lovelace and Sir Edmund Andros, among others, to the office of governor in the colonial days. Instead of plucking some local New Yorker and elevating him to some noble status, they'd give the office to one of their friends, who would go over and run the colony for a few years, and then come back to England (if he didn't die of some disease in the interim).

I can't speak for other British colonies such as Australia and New Zealand, so you'll have to ask somebody else about that.

TL;DR: There were steps toward a peerage system in British North America, but it never went very far, and was very unpopular with the locals. Instead, Great Britain extended the existing peerage system back in England to rule over their overseas colonies, increasing the reach of their wealth and power.

Sources can be found in my original post here.