Blast, while I think this is a very reasonable and thoughtful idea, I'm going to have to say it's very likely a mistake. I'll lay out why below:

Having both taught and observed kids in martial arts, I can say this with a little authority. Most kids aren't even ready at age 6 to begin any serious Martial Arts training. Their attention spans are next to zero, they don't have the physical power or control to handle most maneuvers, and they don't have the mental ability to determine when it's right to cause physical harm to others. Plus if they were to seriously harm someone (alghthough this is unlikely) they may not have the emotional capacity to handle it well.

In my experience, at 3 (my own boy is 3) even if both smart and capable, I wouldn't even think of teaching punching, kicking, or biting, etc. Now, that's not to say that all kids couldn't handle it, but I've seen an awful lot of kids come through the doors of our dojo and we have a policy that they can't start until 6 Yrs. old now. At 3-5, they typically get very little out of it and they can be incredibly hard to train because most Martial arts styles teach people when it's appropriate to use the skills and at that age, they just don't have the situational awareness and decision making processes down yet.

In light of recent tragic events, I think it's prudent to teach kids to run away, to scream for help, and maybe even some very rudimentary self defense such as biting to release someone's grip. But to think that a 3 year old could fend off a gun wielding adult is simply way out of realm of reality. I'm fairly big, strong, fast and capable, and even I would have a hard time against an armed interloper.

Suffice it to say, if you can find a school that caters to kids and does it right (plenty of discipline, yet fun and enthusiastic) like my own school, then you will have to ask the Instructor if they allow 3 year olds. I'm betting more often than not that they won't - the youngest I've heard of is 5 and they have to be emotionally stable (read: not bullies) and "grown up" for their age.

I study Isshinryu Karate and Texas has a decent representation of that style I believe. I find it to be a no-frills street fighting technique that is very very heavy on reality and not full of flash. We don't typically do well at "flash and dash" type tournaments, but at traditional ones, we excel. I find it refreshing to have instruction in an art where progress is mapped to actual ability and not to money. We fail people for moving up in rank all of the time - it's definitely earned. I'd recommend similar schooling for kids. Giving them a higher rank simply because they show up to class and pay their bills is just wrongheaded... avoid these sorts of Martial Arts "mills". If you do enroll your daughter, I recommend that either one or both parents also attend. You'll be able to reinforce their training outside of class, and it's a good bonding experience (not to mention useful for all family members!)

Anyway, my point is that although your DD may be able to learn some things that would be helpful, she may not be able to institute that learning at the proper time due to fear or not understanding the sitaution. Even then, with her size and abilities, it's unlikely she could elude a captor. Trust me when I say I've thought about it fully. I could teach my own child and have opted not to do so, but my advice may be worth what it costs you. <img src="/images/graemlins/smile.gif" alt="" /> YMMV

Edit:
After reading the other replies that were written while I was distracted and typing this up - I will definitely agree that MA will teach discipline, a strong sense of self and duty, and it's excellent physical exercise that teaches control, strength, speed, flexibility, and a very useful skillset. Just don't have the wrong expectation of what your 3 yr. old can do if you choose to enroll her (even if it's at a great school with fantastic instruction).