Hi H.,
Personally, I don't think there's any harm in starting the conversation with her at the age of 3. Will she understand it all - no, but it will give you a starting point to continue to build off of as she gets older. With how affectionate she is, it seems like it might be a necessary thing to do. There are ways to talk about it without making it scary or anything.
There are a few good DVD's out there for her to watch that approach it in a subtle way. I got one called "Stranger Safety". It's a little silly, but it does a decent job grabbing the kid’s attention and getting them to watch. I like how they categorized people as "people we know" (green), "kind of knows" (yellow) and "don't knows" (red). I like how they have the "kind of knows" section particularly because the kids may feel more comfortable with them (making them more vulnerable), but they can be just as dangerous as "don't knows". The categorization setup is easy for me and my 4yo to remember when we talk about it. If you do a search on Amazon.com for "stranger safety DVD" or something similar, it will give you a few options. You can read through the descriptions and other parent’s reviews to figure out if there is one that appeals to you (which you can buy online or somewhere local).
I've talked to my son's preschool teacher about if they teach anything in class, and she said that they do have a safety awareness month where they discuss these things as well. She did advise me though that there have been studies where kids will go through a safety training lesson and then they walk about the door unknowingly being tested on some of these things and said that it was surprising how many of the kids would do something they were just taught not to do. (Keeping in mind too, that some of them did not.) So yes, it is a little young for them to really get it all, but I think that it's more reason to keep discussing it periodically to keep the information fresh in their minds.
I've really found that it works well to utilize time during car rides to talk about various things (since you have them sitting in one spot already and have more of their attention); one of them being stranger safety. (We also talk about fun stuff, like rules of the road, cars, clouds in the sky or anything that comes to mind for either myself or my son(s).) We'll talk about how people can seem really nice and may even have a cute puppy they want you to come and play with or offer a yummy treat, but if they're a "don't know" or even a "kind of know" he can't talk to them unless mommy or daddy are there. I also tell him that it's ok to run away if he feels uncomfortable and even ok to yell if he feels he needs to. I would rather have him feel comfortable doing that than feeling like he has to follow the usual rules even if he's feeling uncomfortable or in an unknown situation. (We've never had any issues with this rule otherwise in case you might think it would.)
**Also, we got a slider lock that we put at the top of our front & back doors so none of my kids can get out or answer the door without me or my husband being there. (Answering the door [or more accurately NOT answering the door] is another safety subject that we discuss.) We got the locks after my oldest son did just what you decribed, which was walk out front with no shoes or socks on and was standing in our driveway when I while I was taking a quick pee break. They sure can move quickly! We haven't had any issues since, and it has stopped many attempts.
You definitely have your work cut out for you with how friendly your daughter sounds. I'm glad you're reaching out to get ideas on how to approach it. I wish you the best of luck in whatever you decide to do.