Can I use jQuery to easily shift li elements up or down?

No native prototypal methods, but you can make one easily:

$.fn.moveDown = function() {
    return this.each(function() {
        var next = $(this).next();
        if ( next.length ) {
            $(next).after(this);
        } else {
          $(this).parent().append( this );
        }
    })
}

$('#menuAbout').moveDown().moveDown()

This uses jQuery.prototype.after

It's actually not that hard. JQuery almost gets you there by itself with the insertBefore and insertAfter methods.

function moveUp($item) {
    $before = $item.prev();
    $item.insertBefore($before);
}

function moveDown($item) {
    $after = $item.next();
    $item.insertAfter($after);
}

You could use these like

moveDown($('#menuAbout'));

and the menuAbout item would move down.

If you wanted to extend jQuery to include these methods, you would write it like this:

$.fn.moveUp = function() {
    before = $(this).prev();
    $(this).insertBefore(before);
};

$.fn.moveDown = function() {
    after = $(this).next();
    $(this).insertAfter(after);
};

and now you can call the functions like

$("#menuAbout").moveDown();