You can use this function, it will avoid counting TextNodes. You can choose to count the children of the children (i.e. recursive)

function getCount(parent, getChildrensChildren){
    var relevantChildren = 0;
    var children = parent.childNodes.length;
    for(var i=0; i < children; i++){
        if(parent.childNodes[i].nodeType != 3){
            if(getChildrensChildren)
                relevantChildren += getCount(parent.childNodes[i],true);
            relevantChildren++;
        }
    }
    return relevantChildren;
}

Usage:

var element = document.getElementById("someElement");
alert(getCount(element, false)); // Simply one level
alert(getCount(element, true)); // Get all child node count

Try it out here: JS Fiddle