Reduced test case of input being covered by keyboard

input_demo.dart

import 'package:flutter/material.dart';

void main() {
  runApp(
    new MaterialApp(
      title: "Input Demo",
      routes: <String, RouteBuilder>{
        '/': (RouteArguments args) => new FlutterDemo()
      }
    )
  );
}

class FlutterDemo extends StatefulComponent {
  @override
  State createState() => new FlutterDemoState();
}

class FlutterDemoState extends State {

  GlobalKey _inputKey = new GlobalKey();

  Widget build(BuildContext context) {
    return new Scaffold(
      toolBar: new ToolBar(
        center: new Text("Input Demo")
      ),
      body: new Material(
        child: new Center(
          child: new Column(
            children: <Widget>[
              new Flexible(
                child: new Container(
                  decoration: const BoxDecoration(
                    backgroundColor: const Color(0xFF00FF00)
                  )
                )
              ),
              new Input(
                key: _inputKey
              )
            ]
          )
        )
      )
    );
  }
}