I've always loved Ropleplaying ahttp://uesp.net/wiki/Lore:Knights_of_the_Dragon. Something about being a guard for the royal Daggerfall family getting mixed up in affairs outside of the city always interested me. Or better yet, I love Bretons, and being a soldier/Agent from Highrock/Daggerfall is cool in my opinion.

Do we know if they're still around during Skyrim's time or not? Is they are not, any other interesting Breton "class" I can roleplay?

I don't think anything has been said about them, but I don't think there's any reason to believe they don't exist anymore. As far as I know the city of Daggerfall hasn't suffered any destruction/siege/sacking/cataclysmic event that would put an end to it. I say as long as there is someone on the throne of Daggerfall, there would be knights of the Dragon, at least by name.

Bretons have some interesting lore surrounding them to make a cool Skyrim character. You have a civil war sparked from a bigger conflict with humans and elves, and Bretons racially are smack in the middle of that. You have "somewhat" Breton kin in the Forsworn, which gives those quests an interesting dynamic on your sympathies. They have a racial power with the word "dragon" in it, which is sort of cool, in a superficial way. Not sure about the Daggerfall faction, but in general, Bretons are just as interesting characters for Skyrim's setting as much as Nords, imo.