Yes, she's most definitely a hen.
Transporting chickens isn't really hard at all. When I've had to take a bird places, I get a large cardboard box and tape all the edges with either duct tape or packing tape, cut some air holes, and put some hay/saw dust/bedding on the bottom. I stick the bird...
She looks too stocky for a game breed... Is she bantam or large fowl, do you know? The coloring is a common EE pattern. She may be a mix.
Good for you for taking her in!