Have you done that? If not, do it.
Did you stop there? Maybe you should pause to ponder the role of the WWW in your child's future.
What about their favorite hobby, pasttime, talent? Might it be natural for your child to someday want to have a website or blog about their favorite activity? Perhaps in the future (like now) kids won't be flipping burgers at Mickey D's or delivering newspapers, like I did when I was 12. Maybe they are future affiliate marketers? At least for making money for car insurance . . .?
What about their career? Are your children of the age where they are talking about a career path or career ideas? Might you do some good by picking up a domain or two related to their possible career interests?
I know. Things change so you don't know for certain what domains to register and you might not know what domains to register for a 2 year old. Still, if you register a domain that's not your kid's love later in life maybe someone else might someday inquire and reimburse your costs.
While you are busy encouraging your children to study hard and all that other stuff you do as a parent you might consider whether having the right website name - today, in 2007 - might afford him or her a bit of a marketplace advantage later in life - in next year.
Domains for kids: It's not just about the names your chose for them.
Some time ago, I tried to register firstnamelastname@yahoo.com for my children and found out that they were all taken; most of the variations, including the middle name, were also taken.
I then registered firstanamelastname@gmail.com.
It looks like because Google used to be more restrict with new gmail accounts, there are more names available.
I bought the lastname[dot]fr because all TLD where taken (by the same guy by the way). Strangely, all his TLDs are redirected to my [dot]fr which is parked currently.
It seems that he forgot to renew the [dot]fr and now it is waiting for me to contact him?
So today, I bought firstname[dot]org today, the only one TLD available with my firstname. I don't like [dot]org...
BTW, I totally agree with what is said above, having a public website about your underage children is to my opinion very bad and should be avoided.
I set up a site with only her name (nothing else, for safety) on it and linked to it from a links page on a site of mine so as to properly age the domain.
That way in 10 years time she can get ranked for mesothelioma if she wants, ha!
By the way it's the oldest's birthday today, he was born on 1/11/1 (or if you are in the US 11/1/1). How cool is that?
Happy birthday Jack!