As far as Japanese martial arts goes, I would avoid anything that ends with "do" which means "the way of" and rather choose the "jutsu" variation which means "the art of".

The difference is that jutsu martial arts are more genuine and closer to their true martial (war) origins while the "do" versions are more adapted to competition thus they left out lethal techniques in favor of sports.

A good example would be Kendo versus Kenjutsu. In Kendo they use light bamboos to fight, while in Kenjutsu they practice more with a real sword and you get used to the weight of the real sword.

Same thing for Judo versus Jujutsu. For serious self defense purposes I would go with Jujutsu where you learn really dangerous tricks while in Judo they removed these tricks so that competition and olympiads are safer.

The one exeption would be Aikido because there's always a simulating aggressor so it's closer to self-defense because they use real life situations.

I would avoid Korean Taikwondo, it's really based around combat competition nowadays where the goal is to gaining points instead of pragmatically neutralize your aggressor and they really favor kicks instead of punches because it originates from a nordic environment with vast valleys and plenty of room for acrobatic kicks and they also had to deal with horse riders. Southern styles like chinese kungfu favors punches and low kicks because they would fight in more cluttered environments like on boats and quays, and would be more suitable for urban self-defense.

But 3 years old is young. I would go for generic self-defense classes aimed at young children.