I'd say YES too, even if your child don't really need it.
My chidren are all bilingual: we live in an english-speaking country, they speak English at school and, well, everywhere ; but at home we speak French, that's the rule. If you want to teach him that other language, then really use it, giving him a lesson once a while in that language wouldn't do much, you'd have to tell him things in different contexts. Like, read him a book in that language, that can be your "night time story", or sometimes tell him things in that language, it doesn't have to be a long conversation, just a few words here and there, for instance if you are cooking pasta you could say "do you want pasta ?[in English] I love pasta ! [in your other language]". (I don't agree with Midas above: yes you can speak different languages to your children, one sentence in one language and the next one is another language, it doesn't matter! learning the language itself is very different from learning when to use it, you will see that later you will have to tell your child "please speak in English, Mr Smith doesn't speak Klingon", which is really another topic than learning Klingon at all -- but indeed you shouldn't mix both languages in one sentence, because then it would be confusing, it would be like teaching another weird language, neither English or whatever-other-language-you-speak...)
And I can see indeed that being bilingual help you to learn other languages. My son especially, he is very good with languages, he is currently learning indonesian at school (just two hours per week or so) and he is doing very well. Because of course he has already learned that things have many names in different languages, once you get that you can call a chair a chaise, a klouk or a whatever, it really doesn't matter.
Plus, you ask if it is worth doing it... Well, if you are speaking a very rare language, you probably need every possible occasions to practice, don't you? It would be good for you. It would also be a great learning experience for your child later, when you tell him why you know that language even though you can't use it a lot.