All of our expensive girl scout trips are paid by using earned cookie money... all of it. Our troop leader gives us a plan for all the activities (..and believe me, there are A LOT- I have yet to know another troop that does HALF of what we do), and says how many cookies need to be sold in order to do all those things... and we also have certain causes we donate to she has up there, and she says how many cookies we need to sell in order to do that. We ALWAYS reach our quota (there are 16 girls... the quota was 208 boxes, believe it or not... and we all made it). That gave us a lot of money to donate and spend on camping trips, and other adventures (we spent the night in a light house once!).
So, I'd have to say that the above idea I mentioned should be addressed with the troop leader, also there is a program that sponsors other girl scouts that can't afford to be in girl scouts... we call it SHARE. we donate to SHARE. I don't think it assists girls that go on trips, but it does help with troop enrollment fees. That could help.
Also, we have no extra money really at all. We live paycheck to pay check, basically... I don't suggest credit cards. It makes it temporarily "okay" to live outside of your means. I cancelled all of our cards years ago. I suggest you do the same. Now, for convenience I only use a check-card.
Not going on that trip would really bum her out. Is there a grandparent you can ask? And maybe you shouldn't go. My daughter has been on plenty of trips with her troop w/o me. I have gone to some, but she does very well without me and most of the girls don't have their mom or dad come. They all do well w/o. My girl just turned 8 a week ago, but she was 6 when she went on her fist no-M. trip.