The number of kids (usually between 5 and 12 years old) that are online and internet literate is large and seems very likely to increase.
Do I think it is healthy for kids to be online that early?
I'm not a child psychologist, so I can't give you an answer based on my research.
1. Introduction (skip to section 2: websites for the websites I recommend)
What I'll say is this: It is (and will become even more so in the future) very important that kids are technologically literate. That involves knowing how to use a computer well and the internet comes hand-in-hand with that.
It is the responsibility of the parents (or parent) to keep their children safe online, especially when the kids are young, growing and very impressionable. Online bullying is just the start of it. Be on top of your child's safety online. I don't think a kid should be allowed alone in a secluded place online at an age till they're older (say high-school age; 15-16 years old). I don't think kids should spend long hours on a computer, tablet or cellphone.
As a tech-head, I'll love my kids to be technology geniuses at 5 years old, but I won't let them get attached to technology. They need to go out and play, get some dirt on themselves, kick a ball, ride a bicycle, have a water-fight, etc.
Technology is important,
2. Websites
Here are a few websites that I think are fun, educational and healthy for your kid when they might want to be grown-up and go online:
1 - For girls like you: http://www.forgirlslikeyou.com/
2 - An addition (math) game: http://www.afunzone.com/Games_in_a_Flash/4/AddLikeMad.html
3 - Fohn.net (check the homepage for other animals too) pictures: http://fohn.net/monarch-butterfly-pictures/
4 - Animal facts: http://www.canadiangeographic.ca/kids/animal-facts/animals.asp
5 - Academic games: http://www.arcademicskillbuilders.com/
6 - Dinosaur pictures: http://www.thedinosaurs.org/ this one might be scary to younger kids... dinosaurs have large teeth :D
7 - Google: www.google.com ← teach your kids how to use google :D (there's more to google than searching for text and images)
These are just a few recommendations.
There are tons out there, just take some time to research and give them to your kid to start with, or maybe create a list of websites that they have permission to visit. Also, consider using a firewall to block certain websites to provide more safety for the kids.
