For more historical background, have a look also at the Genweb project @
http://www.britishislesgenweb.org/dominica/I can see from the timings involved, that men of means could have been invited or persuaded to move to Dominica to take advantage of cheap, or even free, land and labour, and abundant natural resources.
The mention of voting rights for those with land, in what had become a British colony (at that time), makes me think that records might exist in the UK at either the British Library and/or the Foreign Office or relevant embassies.
Somewhere there are dusty volumes containing references to the what why and when concerning Joseph NIXON and his life, but without some specific family details about Joseph NIXON and his parents, this could be difficult.
I note from the original post that no reference is made to why this lookup is needed, and any prior research by the originator - this would help to provide direction and to avoid duplication.
I will carry on with some reading of the old newspapers available online from the British Library and The Times - an endless source of entertainment. I got in to these by going to my library website, going to online resources, and entering my library card number when reaching the relevant resource.
A word of caution, dwalin, it should be them making the running in solving this problem and making this call for help - don't make it your life's work to find the answers. I have a lot more time than you do, but even I have limits - I think.