She looks a lot like the 1906 Singer 27 I recently acquired, except for the thingy on the top of her to the left of the thread. She has a similar bobbin winder and possibly a torpedo bobbin (aka vibrating shuttle) as mine does, too.
Wikipedia lists some knock offs of the Singer 27 here, but I don't see yours mentioned.
http://en.wikipedia.org/wiki/Singer_Vibrating_Shuttle
I didn't have any luck looking up your Red Cross either, sorry. :( Hope you find out more about it. :thumbup: