Hi there, thanks for your query.
I took a look on the White Island Tours website and found this:
"There is no maximum age limit. However, the trip does call for a certain amount of physical ability. The landing involves transferring from the boat to the island via an inflatable craft. Landings vary, depending on conditions. Our preferred method involves stepping from the inflatable onto the wharf or climbing up a ladder (depending on tide), crossing a narrow platform and finally climbing over some boulders. You must be able to walk on an uneven surface for up to two hours and there are no toilet facilities on White Island." - Source
I recommend contacting them directly for more information about the specifics of that tour.