The past few years our family has been in the same boat. I guess lots of people have. Things are improving these days, but during the worst times, several of our friends helped us out, both in person and
anonymously. Did it help? Yes, some months, it saved us. Was it humbling? Oh yes. I can't say I was insulted, but I was definatly humbled. It was good for us though, to be dependant on the charity of others. It makes you empathetic to those around you who are worse off and that feeling lasts once you get back on your feet again.
As far as helping your friend, I think your idea is great. Just what she needs for her birthday. I wouldn't be afraid to let her know it's you either. When someone shows you love, when you really need it, it's nice to know who it was. Either way, it's a good idea. IMO