nextTick

<div id="app">
    <child-component></child-component>
</div>
<script>
    Vue.component('child-component', {
        template: '<div ref="child">Child Component</div>',
        mounted() {
            this.$nextTick(() => {
                console.log(this.$refs.child.textContent); // 'Child Component'
            });
        }
    });
    new Vue({
        el: '#app'
    });
</script>