In this specific case alone Duper intensifies super, usually in a childish, peppy or playful way. One of Barney the Dinosaur's catchphrases is "Super-Dee-Duper!", as if to intensify the sentiment even further. You can see that there's a DVD called Barney: Super-Dee-Duper Day! here. I consider the usage significant, because Barney has been famed as a Public Broadcasting Station mascot throughout the U.S.A. for decades now. You can see the April 11th, 1993 New York Times article TELEVISION VIEW; Of Dinosaurs Why Must This One Thrive? by James Goreman for proof of that.
However, almost as if because it is so cheery, "Super Duper" is rarely used in its literal sense by adults. It is more likely to be said sardonically by them, when they are frustrated, dissatisfied or unimpressed.
Al sardonically joked, "I'm super duper, it's a blast waking up and blowing chunks." He wiped his mouth and sniped, "It's really my hobby." — Who's Laughing Now? by Jefferson Lang, page 208, paragraph 3
If you don't already know, "blowing chunks" probably means puking by the way, 'cause chunks of broken up food come out of your mouth.
Blow Chunks: "1. (idiomatic, slang) To vomit chunks of undigested food."
Excerpt from Wikitionary under the CC BY-SA 3.0 license
That's obviously no fun, so you can tell Al does not really mean what he said.
In this case, I'd make a small wager that she's saying it in an exasperated way, as if the breath has been stolen right out of her because of how very busy and possibly even frustratingly fatigued she is. You'll encounter it from time to time in business settings being used like that, but like Scott said in his comment it's informal.
Some people might even consider habitual use highly annoying. It's especially the case for employers who either feel as if they feel guilty of overworking their employees, or feel as if their employees are not pitching in their fair share and up to the task. Just in order to be on on the safe side, don't tell the boss.