Quick Tips to Child Dialogue

These are more like observations in no particular order or consequence (and again, don't apply to every character), but should come in handy with bringing your character to life. Best of luck!

The younger the child, the more intimate the dialogue.
Consider the difference between a five-year-old child calling his mother "Mommy" and a teenager using "Ma" or "Mother".

Nicknames are important.
They also indicate a closeness between characters or an affinity for another character.

Important things are given important names.
There is a good reason that the child's favorite stuffed dinosaur is named Mr.Dino.

Young children tend to use their own terms to describe something if they don't know the proper term.
Until the child learns the proper term for a magazine, it's a "floppy picture book."

Save the bigger words and the more intelligent speech for the older child.
Younger children have a limited vocabulary because their experience is limited.  There are some exceptions to this, however (like Bean from Orson Scott Card's Ender series who was genetically engineered for exceptional intelligence). Exceptions aside, it can be a bit strange to hear the word "soiree" coming out of the mouth of an eight year old.

Generally, children will start to use slang at school age.
This is because they are interacting with other children and want to fit in.

Younger children are more direct with their questioning and dialogue.
Consider the age-old question "Where do babies come from?". Children generally have yet to understand the importance of appropriateness in a conversation.

Children are generally more honest in their speech.
Deception is learned in time. Children don't see or completely understand the need for lies until they are older.

Children ask questions. A lot of questions.
A child cannot gain a greater understanding of the world around him or her without asking questions to learn how it works.

Mispronunciation is ok.
It's silly to expect that a child should have a complete handle of their given language.

Repetition and mimicry is ok.
Children will often repeat phrases or mimic dialogue of older characters. This can indicate a fondness for the character who is being mimicked, a need for directness, an emphasis on the importance of the phrase, or that the character is simply learning something that he or she has never heard before.