$monthPicker.js

(function ($, moment) {
    var PLUGIN = 'monthPicker';

    function formatValue(value, locale, format) {
        return moment(value).locale(locale).format(format);
    }

    function template() {
        var options = this.options,
            actions = this.actions;

        return $('<table/>', { 'class': options.css.root }).append(
            $('<thead/>').append(
                $('<tr/>')
                    .append($('<th/>', {
                        'class': options.css.prev,
                        'text': options.text.prev,
                        'click': actions.prev
                    }))
                    .append($('<th/>', {
                        'class': options.css.date,
                        'text': formatValue(
                            this.state.value,
                            this.options.locale,
                            this.options.displayFormat
                        )
                    }))
                    .append($('<th/>', {
                        'class': options.css.next,
                        'text': options.text.next,
                        'click': actions.next
                    }))
            )
        );
    }

    function partialUpdate() {
        this.dom.find('.' + this.options.css.date).text(
            formatValue(this.state.value, this.options.locale, this.options.displayFormat)
        );

        this.dom.trigger('change', this.state);
    }

    function incrementMonth(months) {
        this.state = $.extend({}, this.state, {
            value: moment(this.state.value).add(months, 'months').toDate()
        });
    }

    function compose(f, g) {
        return function composition() {
            return f.call(this, g.apply(this, arguments));
        };
    }

    function toDate(dateString) {
        return new Date(dateString.split('.').reverse().join(','));
    }

    $.fn[PLUGIN] = function $monthPickerPlugin(customOptions) {
        return this.each(function () {
            var component = {};
            component.dom = $(this);
            component.options = $.extend({}, $.fn[PLUGIN].defaults, component.dom.data(), customOptions);
            component.state = { value: toDate(component.options.value) };
            component.actions = {
                prev: compose(partialUpdate.bind(component), incrementMonth.bind(component, -1)),
                next: compose(partialUpdate.bind(component), incrementMonth.bind(component, +1))
            };

            component.dom.html(component.options.template.call(component));
            component.dom.on('change', component.options.onChange);
        });
    };

    $.fn[PLUGIN].defaults = {
        value: new Date(),
        locale: 'ru',
        displayFormat: 'MMMM YYYY',
        css: {
            prev: 'prev',
            date: 'date-place',
            next: 'next',
            root: 'table-condensed'
        },
        text: {
            prev: '«',
            next: '»'
        },
        template: template,
        onChange: $.noop
    };
}(window.jQuery || window.$, window.moment));

main.js

$('.month-picker-container').monthPicker().on('change', function (e, state) {
    var date = moment(state).format('MM.YYYY');
    ajaxSend({
        type: 'POST',
        url: 'http://example.com/api/echo',
        data: { data: date }
    });
});