Here are the basics, from Wikipedia:
The HMS Beagle was originally scheduled to leave on 24 October 1831, but because of delays in her preparations the departure was delayed until December. She attempted to depart on 10 December but ran into bad weather. Finally, on the morning of 27 December, the Beagle left its anchorage in the Barn Pool, under Mount Edgecumbe on the west side of Plymouth Sound, on what was to become a ground breaking scientific expedition. After completing extensive surveys in South America she returned via New Zealand, Sydney, Hobart Town (6 Feb 1836), to Falmouth, Cornwall, England on 2 October 1836.
The second voyage of HMS Beagle from 27 December 1831 to 2 October 1836 was the second survey expedition of HMS Beagle, under captain Robert FitzRoy who had taken over command of the ship on its first voyage after her previous captain committed suicide. FitzRoy, fearing the same fate, sought a gentleman companion for the voyage. The student clergyman Charles Darwin took the opportunity, making his name as a naturalist and becoming a renowned author with the publication of his journal which became known as The Voyage of the Beagle.
The Beagle sailed across the Atlantic Ocean then carried out detailed hydrographic surveys around the coasts of the southern part of South America, returning via Tahiti and Australia having circumnavigated the Earth. While the expedition was originally planned to last two years, it lasted almost five.
Darwin spent most of this time exploring on land; three years and three months on land, 18 months at sea. His work made his reputation as a geologist and collector of fossils, and his detailed observations of plants and animals provided the basis for ideas which he later developed into his theory of evolution by natural selection.
So the Toobworld version would have hewn closely to that account, save that Jonathan Brock's father was also on board.