It's difficult for kids nowadays to NOT notice guns, especially for parent(s) who OC (or even CC) a gun on a daily basis. I had this problem since I was open carrying my XD every day starting in 2008 and my 3 kids were younger....
While I agree with the Eddie Eagle thing being a good start geared for the young age, I have to say you hit it on the head when you said:
spillanej wrote:... To me it is obvious that I need to cut the head off of the impending issue by teaching her what a firearm is, what it does, and how to be safe around one.
That's exactly what you need to do.
I would suggest a nice one-on-one sit-down with your child while you're either cleaning, disassembling, reassembling your handgun some day. Explain things. Let your child help with cleaning. But also tell and explain the safety rules, and what to do if a gun is found somewhere.
I believe the key to all of this is taking the "taboo" out of (or removing the "forbidden" stigma from) firearms. I mean, what's the first thing a child will do if you tell him/her "guns are bad don't touch"? Yeah, they're going to go out of their way to find and touch one. Removing the forbidden stigma, and teaching your child one-on-one about firearms and firearms safety is the first step to avoiding a bad accident in the future.
It shouldn't be about "no you can't" but about "sure, under my supervision, what do you want to know?" which creates personal time with you and your child. Tell her any time she has a question about guns to ask you, and you can tell her and/or show her, in a controlled environment. Teaching your child that she can come to you about this sort of subject will prove beneficial in the future with other things, too.
Being out-in-the-open honest about guns, and not all hush hush, with your child will not only get them used to being around guns, learning about the safety rules, etc, but also might take the "curiosity" out of guns so they don't get into trouble when you're not around.
As for hands-on range time, I'd say she's probably too young (mentally, and maybe physically) to shoot, but that doesn't mean you can't take her to one to let her watch, or just hear how loud they are, etc.
So I guess long story short: take the curiosity away from guns, and teach your child gun safety, how guns work, what they are, etc now, since she's showing an interest. Use this as not only an educational opportunity (safety, function, care, etc), but also as more one-on-one time with your child.