<div id="app">
    <div class="dropdown-menu">
        <div class="input-group date">
            <label>from:</label>
            <input size="16" type="text" v-date v-model="queries.start_date" class="form_datetime" readonly="">
            <span class="input-group-addon">
                <span class="calendar-icon"></span>
            </span>
        </div>
        <div class="input-group date form_datetime">
            <label>to:</label>
            <input size="16" type="text" v-date v-model="queries.end_date" class="form_datetime" readonly>
            <span class="input-group-addon">
                <span class="calendar-icon"></span>
            </span>
        </div>
    </div>
</div>

Vue.directive('date', {
    twoWay: true,
    bind: function (el) {
        $(el).datetimepicker({
            format: "mm/dd/yyyy",
            autoclose: true,
            minView: 2,
            daysShort: true
        });
    }
});

var vm = new Vue({
    el: '#app',
    data: {
        queries: {
            start_date: "",
            end_date: "",
        }
    },
    methods: {
        testVal: function () {
            console.log([this.queries.start_date, this.queries.end_date]);
        }
    }
});