If you haven't managed to find enough spare time yet, I thoroughly recommend gradually making your way through this thread. It'll take several evenings, but I promise it'll be worth it. Best thread on Head-fi, in this man's humble opinion!
Make sure you have your creditcard ready, though, coz you're going to find loads of artists whose albums you're gonna wanna buy!
...but don't just take my word for it:
http://www.head-fi.org/t/522812/the-best-female-vocals-your-favorite-female-singers/1260#post_8781627
Indeed, this is one of the VERY few threads on head-fi that is worth reading all the way through.
I don't know enough about your tastes in vocalists to guage what kind of stuff you like, but here's a couple of suggestions, from within this thread:
http://www.head-fi.org/t/522812/the-best-female-vocals-your-favorite-female-singers/690#post_7961906
http://www.head-fi.org/t/522812/the-best-female-vocals-your-favorite-female-singers/1290#post_8862669
http://www.head-fi.org/t/522812/the-best-female-vocals-your-favorite-female-singers/660
http://www.head-fi.org/t/522812/the-best-female-vocals-your-favorite-female-singers/1290#post_8862601
And here's a total wildcard, whom I can't understand but totally dig her husky voice and acoustic backing:
http://www.head-fi.org/t/522812/the-best-female-vocals-your-favorite-female-singers/1260#post_8788369
To tell you the truth, there is such a
wealth of amazing music in this thread that it's almost impossible to choose!
In relation to Emily Barker, it's difficult to think of anyone directly similar, but perhaps one of the following might resonate:
Mary Chapin Carpenter
Kim Richey
Iris De Ment
Kathy Mattea
Natalie Merchant
Sophie Madeleine
Lucy Kitt
Nataly Dawn