Aaryn Costello is searching for the perfect dress, a 30-inch-long light-blue number with a sparkly bodice and a detachable white cape.

That would be the Princess Elsa dress from the Walt Disney Co. hit “Frozen,” the most sought-after fashion item among the kindergarten set. Stores across the U.S. are sold out, and originals are being offered for as much as $1,600 on eBay. Desperate parents are sewing their own or shelling out up to $225 for replicas on sites like Etsy.com.

“Every mom in the world is dying for this dress,” said Costello, a Los Angeles marketing consultant with a “Frozen”-obsessed 4-year-old.

“The property is hot,” said Sean McGowan, a toy-industry analyst at Needham & Co. in New York.

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Retailers didn’t order enough of the gowns, said Dena O’Loughlin, director of marketing for Disney-licensed girls costumes at Jakks Pacific. Stores sold out in January of Jakks’ version — suggested retail price: $20 — and the company is working with merchants to bring in reinforcements by air and boat from factories in China.

“It has been challenging to keep up with demand,” O’Loughlin said.

Buyers didn’t anticipate how big “Frozen” would be and stocked about as many of the gowns as they did Rapunzel outfits from Disney’s 2010 “Tangled,” O’Loughlin said.

After the movie opened in the U.S. on Nov. 22, “Frozen” went on to become the top-grossing animated film of all time

As sales began to climb and orders poured in after the Christmas holiday, Jakks had trouble restocking because of Chinese New Year, which shut down manufacturing in that country for a month until mid-February. It will take up to three months for retailers to receive shipments of goods made in China, so prices aren’t likely to thaw until summer.