Here's a simple class you can use to compare dates; the convert function has been adjusted to accommodate your format:
<script type="text/javascript">
    var dates = {
        convert:function(d) {
            return (
                d.constructor === Date ? d :
                d.constructor === Array ? new Date(d[1],d[0],d[2]) :
                d.constructor === Number ? new Date(d) :
                d.constructor === String ? new Date(d) :
                typeof d === "object" ? new Date(d.year,d.month,d.date) :
                NaN
            );
        },
        compare:function(a,b) {
            return (
                isFinite(a=this.convert(a).valueOf()) &&
                isFinite(b=this.convert(b).valueOf()) ?
                (a>b)-(a<b) :
                NaN
            );
        },
        inRange:function(d,start,end) {
           return (
                isFinite(d=this.convert(d).valueOf()) &&
                isFinite(start=this.convert(start).valueOf()) &&
                isFinite(end=this.convert(end).valueOf()) ?
                start <= d && d <= end :
                NaN
            );
        }
    }
</script>
Credit for this class belongs to @some: https://stackoverflow.com/a/497790/879420