But she did not realise how close she was to the platform edge, British Transport Police (BTP) said.
The buggy wheels went off the edge - and she, the buggy and the child fell on to the track.
The child's father immediately jumped down to help them, but a train was on the way and they dived for cover.
BTP said: "When they saw a train coming, all three were extremely fortunate in being able to move into a pit under the track and the train passed safely over the top of them.
"Amazingly none of them were seriously hurt, but as a precaution they were taken to hospital for check-ups."
SKY News.