That's simply not true. It wasn't until the 26th amendment, in 1971 that the right to vote was set as 18 in the US. Before that even that right was dependant on state based laws. (Note that under 18's don't have the right to vote at all)
OTOH, Tinker v. Des Moines Independent Community School District[1] holds that children DO have the right to freedom of expression.
http://people.howstuffworks.com/do-children-teenagers-have-c... is a pretty reasonable discussion
[1] http://en.wikipedia.org/wiki/Tinker_v._Des_Moines_Independen...
If a "right" can be signed away, it's not really a right. I recall reading about a case where a woman agreed, in writing, to waive her right to maternity leave under FMLA. She then changed her mind, and the employer sued and lost on the grounds that rights cannot be signed away.
Looked at from that lens, you're arguing that a child's rights can be signed away. My argument is that therefore they aren't rights.
Thus in most of the world today, you cannot willingly sell yourself into slavery.
But many of these rights (eg, the right to carry arms, the right to enter into contracts, etc) are limited to adults.
I think my main point still stands. Her view on appropriate punishment is only a part (I'd argue a small part), of the overall consideration.
If we look beyond the gag order and her constitutional rights, I can play the devil's advocate and say that juvenile delinquents deserve special consideration. Should the poor/horrible decisions of a child/teen ruin their life for good? Or should they get a second chance? 10 years from now a potential employer might Google their names and decide not to hire them because of this. I'm not sure that's justice.
As a result, a post-trial gag order is going to be exceptionally hard to justify because of 1st Amendment grounds.
Nebraska Press v. Stuart (1976) overturned a judge's gag order against the press. The entire point of a gag order or "protective order" is to protect the 6th Amendment rights of the defendant. The Supreme Court and Appeals Courts are clear in this regard.
The point is, this girl should take this case to Federal Appeals Court -- she'd win because the judge has no Constitutional leg to stand on, especially since this is post trial/conviction. She should have a right to speak about her experiences wherever and to whomever she pleases. Her right to speak cannot be infringed if there is no underlying Constitutional conflict (i.e. right to a fair trial, etc.)