Okay, stats time!
Here's the list of ladies who medaled at their first Worlds since 1961:
1990 Holly Cook, USA, bronze. This would be Cook's only time at Worlds.
1991 Tonya Harding, USA, silver. Harding never medaled again at Worlds.
1991 Nancy Kerrigan, USA, bronze Kerrigan got a silver in 1992 Worlds.
1993 Oksana Baiul, UKR, gold. This would be her only Worlds.
1999 Julia Soldatova, RUS, bronze. This would be her only Worlds for Russia. She would also skate for Belarus, but she would only place 18th.
2006 Kimmie Meissner, USA, gold. Meissner would never medal again at Worlds.
2007 Mao Asada, JPN, silver. Asada won in 2008 and 2010. But she was OTP in 2009, 2011, 2012.
2007 Yuna Kim, KOR, bronze. Kim has medaled at every Worlds she competed in -- bronze in 2008; gold in 2009; silver in 2010 and 2011
So consider this out of eight woman who won medals in their Worlds debut:
Three or 38 percent of those debut winners (Kerrigan, Asada and Kim) medaled again.
Half of them have Olympics medals. (Kerrigan, Baiul, Asada and Kim)
Only two won Olympic Gold (Baiul and Kim)
Most of the Olympic/recurring Worlds winners had respectable top 5 or top 10 debuts before winning their string of medals.