The child, Rachel Kendall, was wearing a lifejacket but became trapped under the trolley after it slipped over the edge of Kemp's Quay in Bitterne, Southampton, as the family boat was being unloaded on Sunday night.
Her sister, Lisa, five, who was also sitting on the trolley, and her mother, Janet, fell into the water, but they were saved as they floated in their lifejackets.
Rachel became trapped under the trolley. Two passers-by managed to free her, but she was pronounced dead shortly after arrival at Southampton General Hospital.
A police spokesman said the accident happened as Janet and Graham Kendall and their four daughters, Jeanette, 12, Claire, 9, Lisa and Rachel, from Boscombe, Dorset, were unloading their boat after a trip to the Isle of Wight.
'They were making several trips along the quay with their luggage and for some reason the trolley slipped off a ramp and fell into the water.
'The mother was distraught and was trying to tell the people rescuing them that another of her daughters had fallen in. But by the time they managed to get her out it was too late.'
Robert Kemp, owner of the quay, said: 'It's the worst thing that's happened here in 40 years. Normally lifejackets should have been good enough. It's so awful.
'The woman was on the quayside and she was gesticulating at the water saying 'My children are in there'. She then started shouting, 'My baby, My baby'.
'A chap got in the water and felt the trolley with his feet. He pulled the trolley up and the baby was in it. The little girl was already blue and the man gave her mouth-to- mouth resuscitation. He knew almost immediately she was dead.'Reuse content