The family will get to meet Sinbad, the comedian/actor, and either have lunch with him or visit him on a Hollywood film set.
The shopping spree will take place at a California mall during their visit.
The Rohms are planning to take the two-week trip in May.
Although the trip originally was planned for four people, the Rohms and the television network have worked it out so that the family of five can go.
The family is considering driving out instead of flying, as previously arranged, so they can visit Yellowstone National Park and other sites.
The contest, a promotion for the Fox Children's Network, required entrants to submit postcards.
Dorothy Rohm sent in two postcard contest entries for each of her three children, Jessica, Brian and Adam, 3, before Christmas.
Jessica found out she was the winner when the television network telephoned her on Jan. 21.
Hers was the winning entry from among 110,000 entries, said Karyn Adelstein, assistant to the director of network promotion at Fox Children's Network.
"They said, `You won,' and I started screaming," Jessica said. "First I ran to them (parents) and then I ran up to my brother who was in bed because he was sick."
Their daughter's excitement interrupted a meeting the Rohms were having with their insurance agent at the kitchen table.
Dorothy Rohm said she picked up the telephone and the Fox official told her Jessica was the contest's grand-prize winner.
He asked her to put Jessica back on because they wanted to make a voice recording of her reaction to the news.
Rohm's recorded reaction was heard on television four times at the conclusion of different programs.
"We kind of didn't believe it until we got all of the paperwork," Dorothy Rohm said.
Rohm, a third-grade student at Southern Fulton Elementary School, said news spread fast after she learned she'd won.
At school the next day, Jessica said she told the principal, then her teacher, then the whole class. Her brother told friends in the fifth- and sixth-grade wing, and her mother, who volunteers at the school, confirmed the information.
"About five or six people want me to get something for them," Jessica said.