She did see Melody as a child (not only as a baby) on several occasions:
- In "The Impossible Astronaut"/"Day of the Moon", she saw the original (Sydney Wade) incarnation. Although the Amy we saw in those episodes was a Ganger, the real Amy was linked to her Ganger & saw what the duplicate saw.
- In "Let's Kill Hitler", Amy & Rory learned that the Mels who had grown up with them through childhood & adolescence was also an incarnation of Melody. As Mels herself put it, just before she regenerated into her River Song incarnation, Amy & Rory "got to bring [her] up, after all."