JSFiddle - React, Tailwind, and code Playground

HTML

<script src="http://momentjs.com/downloads/moment.js"></script>
<input type="text" id="txt-entrada" onkeyup="adicionarHora()" value="24/05/2015 23:00:00" placeholder="Entrada" />
<input type="text" id="txt-saida" placeholder="Saida" />

JavaScript

var entrada = document.getElementById("txt-entrada");
var saida = document.getElementById("txt-saida");

function adicionarHora() {
    // converte string em data
    var data_entrada = moment(entrada.value, "DD/MM/YYYY HH:mm:ss");

    // define o valor da saida
    saida.value = moment(data_entrada).add(1, 'hour').format('DD/MM/YYYY HH:mm:ss');
}