Under MLA, the year used in a citation is the date of publication for the work you're citing, not the original year of the work in question.
The reason for this is because a number of things could change between different publications: different forewords, translations, prefaces, grammar and spelling changes ...
The example format for your book would be something like:
Dostoyevsky, Fyodor, and Constance
Garnett. The Karamazov Brothers.
Ware, England: Wordsworth Classics,
2010. Print.
(If it helps, I use http://www.easybib.com/ for generating bibliographic references and citations.)
Update: Sorry, forgot to add. MLA uses (Author Page) for in-text citations if I'm not mistaken. If you want to use (Author, Year), it should be year published, not the original year first published.
Another Update: Last one, I promise! In your example, you appear to want to show the year it was first published as a fact, not as an in-text citation, so you're better off writing something like:
Dostoyevsky, in his 'The Brothers
Karamazov', first published in 1879,
[..]
Or alternatively:
Dostoyevsky, in his 'The Brothers
Karamazov' (first published in 1879),
[..]