I am going to paint mym daughter's room and will be going from blue to yellow.
Is it necessary to put a coat of primer first?
You normally do not need a primer when painting latex over latex, but in this case I would prime the walls white as yellow does not cover very well. You will use a latex primer but do not let the paint store tint it close to the color as it will not work as well as leaving it white.
I would definetly use a layer of some high-hiding primer like Zinzer or Kilz. The extra $15 may save you 2 extra coats. Yellow does't cover dark colors well, you will see the layers.
As great as the Zinsser and Kilz products are at sealing they do not cover very well as that is not what they are suppose to do. The Zinsser rep says that her primer is not made to cover but that is left up to the finish paint. In your case you need coverage and not sealing and or stain killer properties. So ask the paint store to sell you their best covering latex primer.