Australia could have been Iceland
In my studies on medieval north-western Europe I have also looked at the Vikings, who had an enormous impact on this region between the years 800 and 1100. In the early 800s they reached Iceland which, at that stage, was still uninhabited except from two small communities of Irish monks who had arrived not long before. By 1100 the Viking era was over and the Scandinavian raiders and traders had either left the countries they had occupied or their people had been fully integrated in the local population. The Scandinavians however, did hang on to Iceland , ruled by Denmark, than by Norway and eventually again by Denmark,
By 1200 the Medieval Warm Period had ended and this make it much more difficult to maintain (shipping) communications and for the following centuries Iceland remained a rather isolated part of the Danish empire. As a matter of fact there were several occasions where the Danes considered to get rid of Iceland. Very similar to what happened to some of their other possessions such as Shetland and Orkney.
In the 1780s there was another event that triggered e review of the territory. England was in search of a new penal colony and Iceland was considered as an alternative to Botany Bay in distant Australia.
The plan was to offer Denmark the uncolonised West-Indian Crab Island, situated between Puerto Rico and St Thomas, close to some of the other Caribbean possessions Denmark already had in this region. Denmark had already several times tried to take control over the island but this was opposed by Britain and Spain. The negotiations were led by the Scot John Cochrane, a son of the 8th Earl of Dundonald. He enjoyed the support of Henry Dundas, the secretary of war who was one of Prime Minister William Pitt’s closest allies in the British government. John hoped that the deal with Denmark would help him in becoming the Earl of Iceland.
Cochrane argued that the convicts could be employed in the fishery and would thus have a useful trade upon their release. The fisheries would also be a good training ground for the British navy and could deliver hardened seaman to them. Because of the lack of timber on the island, escape would be very difficult. The scheme did not go anywhere and eventually Cochrane gave up.
The last time Britain showed interest in Iceland was in 1860s, but also this time that came to nothing. The country became an independent republic in 1944.
Source: Der dänische Gesamtstaat: ein unterschätztes Weltreich? By Eva Heinzelmann, Stefanie Robl, Thomas Riis, 2006.