I know this is an old thread, but it's only $10 to have the vet put her to sleep. Hopefully they are well trained in it, but ours only took one stick. They inject the same stuff they use for dogs and cats in the heart because the veins are really hard to hit. I would consider that if you don't want to set up the dry ice or CO2 chamber.

Don't let her go, and IMO don't fix her ear infection, put her to sleep.