Anderson wasn't sure how the incident happened but said the sea and weather conditions weren't an issue.
"I was tracking on my two GPSes and I still can't understand why I hit the rock.
"I had a track and global positioning chart and I also had another GPS beside that," he said.
The skipper was unaware of the Queen Elizabeth's offer.
"My first priority was to the people on board and my son. I was worrying about where we were on the rocks, damage to the vessel, comms and where my lighting was," he said.
North Shore Rescue sent two volunteers on to the rocks to assess the situation. The four men and the child on board were shaken, anxious but unharmed. All five were wearing life jackets.
Coastguard operations manager Ray Burge said the skipper had acted calmly after the incident.
"It was a fantastic response by the volunteers who quickly got the situation under control," he said.
"The skipper had lifejackets for everyone and was able to make the distress call to get help.
"This makes a huge difference to our ability to respond and get the positive outcome after what was no doubt a frightening experience for those on board."
Anderson was extremely grateful to the Coastguard for their help.
"Coastguard have done excellent work and I take my hat off to them. They will be getting a very reasonable donation for their time and efforts," he said.
"They did everything they could and all my crew on board did what they were told."