A photographer automatically owns the copyright in an image he/she has created, and may publish it at will - even if the person in the photograph hasn't consented. This is the rule that enables newspapers to publish pictures of Film and TV personalities emerging from nightclubs a little tired and emotional. It's also the rule that means wedding photographers own the copyright of your wedding pictures - you don't unless you have arranged otherwise.
Images of children are no different - you may legally publish them without anyone's consent, provided you own the copyright, or have obtained a copyright licence from the original photographer or his/her agents or assignees.
Common sense dictates that you should proceed with caution. There's often a fine line these days between an inncocent image of a child and one which might appeal to paedophiles - and you should err on the side of caution. No decent person wants to risk offending a child or its parents by publishing images on the internet without consent, and it makes sense to ask first. A verbal consent is quite sufficient.