Miller said she didn't know initially why guests were being gathered on deck.
"Before we went to bed, there was a pretty bad storm, and the ship was really rocking, so our first thought was that we were sinking, because they said 'life jackets' and run," Miller said. "We got up to the deck, and we see the lifeboats being lowered down. ... We didn't know what was going on for about a half-hour, when they made an announcement that there was a fire."
She said the crew handled the situation well.
"Even though it was terrifying, they tried their best to make everyone comfortable. They're so well-trained that I felt confident that we would be OK," she said.
The 916-foot-long ship was launched in December 1996 and refurbished in May 2012, the company said.
Several cruise ship incidents have made headlines in the past year and a half.
In January 2012, 32 people died when the Costa Concordia capsized off Italy's coast.
In February this year, an engine room fire left the Carnival Triumph adrift in the Gulf of Mexico, with passengers reporting overflowing toilets and human waste running down the walls in some parts of the ship.
In March, the Carnival Dream cut short a Caribbean cruise, with Carnival reporting that the ship's emergency generator failed. And this month, authorities say, a man and a woman on the Carnival Spirit went overboard off Australia's coast; they are presumed dead.