React, Webpacks and Babel: "You may need an appropriate loader to handle this file type."

Question

I know this is a fairly common error and is a result of poor configuration in config file. I've searched few posts but can't seem find the right solution. I'm fairly certain this was caused after installing two specific dependencies: babel-preset-es2015 && babel-preset-react.

I've tried uninstalling / re-installing, with no resolve.

I was following this tutorial.

Thank you for any help in advance.

The error code reads:

    Version: webpack 2.1.0-beta.22
Time: 55ms
    Asset     Size  Chunks             Chunk Names
bundle.js  2.68 kB       0  [emitted]  main
   [0] ./public/app.js 246 bytes {0} [built] [failed] [1 error]

ERROR in ./public/app.js
Module parse failed: /Users/user/Desktop/Development/CCJournal/public/app.js Unexpected token (5:1)
You may need an appropriate loader to handle this file type.
| 
| render(
|   <div>
|       <h1> Testing </h1>
|   </div>,

Webpack.config.js

module.exports = {
entry: "./public/app.js",
output: {
    path: __dirname + "/public",
    filename: 'bundle.js'
},
module: {
    loader: [
        {
            exclude: /(node_modules)/,
            loader: 'babel', 
            query: {
                    presets: ['es2015', 'react']
            }
        }
    ]
},
watch: true
}

App.js

import React from 'react'
import { render } from 'react-dom'

render(
    <div>
        <h1> Testing </h1>
    </div>,
    document.getElementById('app')
)

Package Json

  {
  "name": "ccjournal",
  "version": "1.0.0",
  "description": "Test Assignment",
  "main": "index.js",
  "scripts": {
    "webpack": "webpack",
    "test": "echo \"Error: no test specified\" && exit 1"
  },
  "author": "",
  "license": "ISC",
  "dependencies": {
    "babel": "^6.5.2",
    "babel-cli": "^6.22.2",
    "babel-core": "^6.22.1",
    "babel-loader": "^6.2.10",
    "babel-preset-es2015": "^6.22.0",
    "babel-preset-react": "^6.22.0",
    "express": "^4.14.1",
    "pug": "^2.0.0-beta10",
    "react": "^15.4.2",
    "react-dom": "^15.4.2",
    "react-redux": "^5.0.2",
    "redux": "^3.6.0",
    "webpack": "^2.1.0-beta.22"
  }
}