You won't get any money until ur a teenager, then the king will give you (1000) I think, so that you can buy some food. It is though gonna be tough for the first generation teenager, since it then won't get any money until it's an adult.
If you take good care, and get lots of points, your tama will get three works as an adult (one for skill points, two for money) then you can go to concerts, and believe me, ur tama's gonna get rich!
If you don't get through pro debut, I think you'll still have the works though, but no concerts!
Then on second generation, depending on if you have the newer or older music star version, your parent will either take all money and then send it to you as a teen, or, you'll get to keep half of it.
(I know this got a bit too long but I anyway hope I helped!)