Eugene,
All of the answers here will no doubt provide you with some very good training. I would second any recommendations for a first aid class as well.
Glocker36 pointed out that you should also obtain a first aid kit, or even make your own. Do become familiar with it as suggested and yes plenty of forums are filled with plenty of good intending people who have no knowledge on how to use one. There are plenty of us on here who will critique it for you. Buy or even make a few more kits as well. One for each vehicle you own and a spare. My neighbor's son took theirs on a boy scout outing or some such and came home without it. Mom was not too pleased. I had to help her put another together, which I don't mind, but she worried it would happen again. She then went to Costco and bought 3 in a bundle pack. We built one good kit and used one for her Jeep. The third will be used when her son goes camping again this summer.
If you contact the fire department then you might also ask them if they'll teach a class on fire extinguisher use. Even if they do not teach the first aid or CPR they may hold a class for fire extinguisher use. Homeowners and businesses have them and I would say a vast majority of people have no idea how to safely and effectively use them. Alan and Martin may be able to provide better information on this than I am able to.
Glad to hear that your daughter will be okay.
Stargazer