No, it is not a good idea.

First of all, it is unconstitutional on many levels:

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof;

Right there it states that one cannot impost any restrictions whatsoever on the free exercise of religion. Whether you like it or not, this addresses children as well.

abridging the freedom of speech

Such a law could, in theory, prohibit parents from even having the freedom to speak to their own child regarding a religious topic!

or of the press

Not only does this mean that one can publish that which one will, but does it not also mean that one can read what one wills?

or the right of the people peaceably to assemble

When people congregate at church, they are peaceably assembling. Such a law as that which was petitioned would in essence ban children from entering a place of worship.

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But you'll say "Dawkins is British; Britain doesn't have a constitution."

Well, the answer is no, Britain does not have a constitution. However, what I said of the constitution goes hand-in-hand with what I could have said regarding Article 9 of the European Convention on Human Rights and articles 18, 19, and 20 of the Universal Declaration of Human Rights which states, respectively:

European:

Article 9 – Freedom of thought, conscience and religion 1. Everyone has the right to freedom of thought, conscience and religion; this right includes freedom to change his religion or belief and freedom, either alone or in community with others and in public or private, and to manifest his religion or belief, in worship, teaching, practice and observance.

2. Freedom to manifest one's religion or beliefs shall be subject only to such limitations as are prescribed by law and are necessary in a democratic society in the interests of public safety, for the protection of public order, health or morals, or for the protection of the rights and freedoms of others.

United Nations:

Article 18

Everyone has the right to freedom of thought, conscience and religion; this right includes freedom to change his religion or belief, and freedom, either alone or in community with others and in public or private, to manifest his religion or belief in teaching, practice, worship and observance.

Article 19

Everyone has the right to freedom of opinion and expression; this right includes freedom to hold opinions without interference and to seek, receive and impart information and ideas through any media and regardless of frontiers.

Article 20

1. Everyone has the right to freedom of peaceful assembly and association.

2. No one may be compelled to belong to an association.

Well, Terminator here seems to have the base pretty much covered... even though this is his own debate. Right. I was just going to say it'd be pretty fucked up, because that's basically telling people they can't tell their children their heritage and what they believe. Your beliefs and your heritage are really the only thing you have in this world that are impossible to take away.