Sure, it's a good idea and, perhaps a nice gift, to register your child's name as a domain name.
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.