In an email, Carnival spokesman Vance Gulliksen said he was unaware of the "Duck Commander" cruise.
"Theme cruises are contracted by independent third parties and not through the cruise operator," said Gulliksen.
Brown said Premier had not communicated with Carnival following the firestorm sparked by Robertson's remarks.
"We completely chartered the Carnival ship, so it's not a Carnival cruise per se," she explained.
In the interview with GQ Magazine, Robertson described gays as sinners, implied various non-Christian cultures were inherently murderous, and said African Americans were "singing and happy" during the Jim Crow era. However, Brown said Robertson's comments were not a concern for Premier.
"We're a small company that is doing this cruise and actually we've had absolutely no cancellations since this so, you know, we're just doing the cruise," Brown said.
The "Duck Commander" cruise will feature "question and answer sessions" and "autograph sessions" with Robertson and other members of his family. There will also be musical performances by "American Idol" winner Scotty McCreery and Mac Powell of the "Christian rock band Third Day." Taking off from Miami, the five-day cruise includes stops in Key West and Cozumel.
Brown expects the cruise will attract a diverse array of passengers.
"We obviously don't ask people their sexual orientation or race or anything like that when they book a cruise, but I imagine that we'll have all kinds of people," said Brown. "I think Joe Blow American is just keeping their nose down and doing what they need to do."
The "Duck Commander Cruise" is sold out and there are "hundreds" of people on the standby list, Brown said. Standby tickets for the cruise range from $2,798 to $3,718 for an all-inclusive, double occupancy package.