At my daughter's Dojo, they start kids at 5 years old.
This is due to developmental age/ability to follow directions/attention span per age/toilet trained or not/the motor-skills and coordination ability of kids this age/the development of the bones & growth plates & the fact that young children can often take more 'pain' and hyper-extension of their joints... because their bones/tendons/ligaments are more loose and flexible at this age. Thus, more injuries can happen, for example.
Versus with an adult, they will experience 'pain' more readily and thus, will at-will 'stop' the movement, etc.
At 3 years old, the class/instructor will teach with the age parameter in mind. They should. And, it will probably be mostly, very elementary expectations, at first.
So keep that in mind.
My daughter, LOVES Karate.
She has been taking it for about 2+ years now. SHE loves it. So we continue with it, for her. She is now a Blue Belt.
Her Dojo does not just hand out belt color promotions... willy-nilly nor like candy. The child... HAS TO EARN IT. If not, they stay at their present belt level.
It is hard work.
At 3 years old, do not expect.... a highly skilled level of ability.
And, if you just want your child to be active in a 'class', there are other options.
As for 'discipline' & "respect'.... it does teach that... but each child has their own ability to adapt to that, or not. Some kids, CANNOT take it... nor the "strictness" of the Sensei or teachings. Bear that in mind.
For example: some kids in my daughter's class, stopped taking classes. Because... they could not handle, being 'corrected' or told to behave. Nor could they adapt to the high structure, of the classes.
It is age and maturity. And the realization... that with martial arts.... there are expectations.... as a philosophy and skill.
At my daugther's Dojo, they do NOT, 'baby' the kids. It is not Preschool.
It is traditional teaching. With traditional martial arts, expectations.
Some Dojos... are more.... loose in teaching young kids.