Peach’s Up Special has her leap into the air with her parasol and gently float back down.
The first time Peach used a parasol to float was when she jumped from her castle to join Mario on his adventure in Super Mario RPG. The parasol would then go on to become a weapon in the game and a staple of Peach’s character going forward.
While Peach will often use her magic/dress to float through the air in games like Super Paper Mario and Super Princess Peach, she relies on a parasol. The design of the parasol in Smash is actually pulled from Super Paper Mario.
Even more interestingly, data in Super Smash Bros. Brawl’s code suggests Peach was originally intended to use Perry, the magical talking parasol from Super Princess Peach.