In my admittedly limited experience, dueling, as in one on one pistols at dawn (or swords, lasers, whatever), the classic view of dueling requires two things. Lots of privilege, and lots of boredom.
In EvE, I can only see the Amarr and Galente having the right mix for these among the empires. The Minmatar or Caldari, not so much. The Minmatar yes I can see having one on one fights over something, sure. But I can't see them having the privileged class that would lead to a "I demand satisfaction" duel. Fights with rules, to the touch, cut, blood, death, sure.
Caldari, sort of the same thing. I could see this among what passes for the disaffected youth, but it would be more gang fight (drawing this from too many old moives and anime) than one on one with rules and such.
Galente, oh yes. Going off A Burning Life, the Galente are a people who will literally re-build themselves because they can. More than enough wealth, privilege, and boredom there that people would cook up dueling. I could see the fights being tracked on the web, famous fighters having groupies, being the rock stars of their nitch, and all completely illegal under Federation law but allowed to go on anyway on any planet.
Amarr, it could happen, more than enough prestige and power. But I question the boredom side of things. I don't think enough Amarrians' would be allowed to become bored enough with life to start this, or if they did, I don't think they would risk their own necks. But that may just be my knee jerk reaction to a slave owning culture, I start drawing parallels with Rome and bread and circuses.
IMHO, YMMV, etc.