Apparently I'd be Abigail. I don't associate Abigail with babies at all, though come to think about it I do know some people with babies with Biblical names despite not being at all religious, so maybe it's a trend.

2000s: Kayla (which is a name I do associate with small children, thinking about it)
1990s: Amber
1980s: Angela
1970s: Susan
1960s: Barbara
1950s: Brenda
1940s: Margaret (could live with that)
1930s: Ruth
1920s: Anna (could also live with that, though had been hoping for something a bit more flapperish)
1910s: Alice (another name I associate with children, though I do know several Alices who are my own age or slightly younger)
1900s: Lillian (annoying to constantly be spelling it, would prefer Lilian)
1890s: Bessie. Um.