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Elon Musk 's transgender daughter Vivian just made her New York Fashion Week debut ... strutting down the runway for the Alexis Bittar show in a shimmering pageant-style dress.

Check out the pics from Friday -- Vivian looks calm, cool and collected as she models a sparkling red dress with ruffled short sleeves and a Miss South Carolina sash. Shutterstock

The showcase is fitting for Vivian -- who is estranged from her famous father who disproves of her transition -- because its "MISS USA 1991" theme is about "misogyny, unchecked predators, objectification and trans rights," according to the NYC-based brand.

In a backstage interview with Nylon, Vivian says the states chosen for the sashes are where trans right are curr

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