Originally posted by twintastic2 Lily | Flickr - Photo Sharing!
This is more typical and yes it does happen outside but a lot less. I noticed this one said it was not stabilised which was interesting as I thought I'd waited...guess not! Probably the issue?
SR not kicking in might have been a factor here but even if it had activated 1/13sec is way too long of a shutter speed when taking a portrait of a kid, even one trying to stay still. SR doesn't slow down a moving target, you need a tranquilizer for that. This might be a nono with your own children though.
I'd go with a faster lens if available. Failing that, bump up the iso, a grainy shot is usually much better than a blurry one. Or add light. Knock out a wall if you have to. Photography is a great reason for home renovation- don't be afraid to add some huge windows or skylights.
Indoor low light conditions are tough and near impossible to get sharp, clean results of moving targets with the slow kit lens. It's a matter of picking a compromise between the noise of higher iso and low enough f-stop (and the lower depth of field this gives) to get a high enough shutter speed that you are comfortable with.
Note the photo you liked involved the flash, which has a very short duration effectively freezing any motion of your daughter and any camera shake. The ambient light portion of the exposure may still cause some blur, but given that the flash is a fair bit stronger here and you are at a safer 1/30s, it will hardly be noticeable.