To get the children nodes, use obj.childNodes, that returns a collection object.
To get the first child, use list[0], that returns a node.
So the complete code should be:
var div = document.getElementById('header-inner');
var divTitleWrapper = div.childNodes[0];
var h1 = divTitleWrapper.childNodes[0];
If you want to iterate over all the children, comparing if they are of class “title”, you can iterate using a for loop and the className attribute.
The code should be:
var h1 = null;
var nodeList = divTitleWrapper.childNodes;
for (i =0;i < nodeList.length;i++){
    var node = nodeList[i];
    if(node.className == 'title' && node.tagName == 'H1'){
        h1 = node;
    }
}