Error : NoSuchMethodError, The getter 'index' was called on null

The issue here is the DefaultTabController context is the same as in which DefaultTabController.of(context).index is defined.

To solve the error - you need to define DefaultTabController in the parent context.

Your code working:

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: DefaultTabController(    // Add here
        child: Login(),
        length: 2,
      ),
    );
  }
}

class Login extends StatefulWidget {
  const Login({Key key}) : super(key: key);
  _LoginState createState() => _LoginState();
}

class _LoginState extends State<Login> {
  double _containerHeight = 300;

  @override
  Widget build(BuildContext context) {
    return Scaffold(                      // Remove from here
        body: Container(
            child: Padding(
      padding: const EdgeInsets.all(10.0),
      child: Column(
        children: <Widget>[
          SizedBox(
            height: 150,
          ),
          Container(
            padding: EdgeInsets.only(left: 20.0, right: 20.0),
            child: Column(
              children: <Widget>[
                Container(
                  height: 52.0,
                  decoration: BoxDecoration(
                      color: Colors.grey[200],
                      borderRadius: BorderRadius.all(Radius.circular(100.0))),
                  child: TabBar(
                    indicatorSize: TabBarIndicatorSize.tab,
                    indicator: new BubbleTabIndicator(
                        indicatorHeight: 45.0,
                        indicatorColor: Colors.blueAccent,
                        tabBarIndicatorSize: TabBarIndicatorSize.tab),
                    labelColor: Colors.white,
                    unselectedLabelColor: Colors.black,
                    onTap: setAnimatedContainerHeight(
                        DefaultTabController.of(context).index),
                    tabs: <Widget>[
                      Tab(text: 'Login'),
                      Tab(text: 'Register'),
                    ],
                  ),
                ),
                SizedBox(
                  height: 20.0,
                ),
                AnimatedContainer(
                    duration: Duration(seconds: 1),
                    padding: EdgeInsets.all(40.0),
                    width: double.infinity,
                    height: _containerHeight,
                    decoration: BoxDecoration(
                        color: Colors.white,
                        borderRadius: BorderRadius.circular(8.0),
                        boxShadow: [
                          BoxShadow(
                              color: Colors.black12,
                              offset: Offset(0.0, 15.0),
                              blurRadius: 15.0),
                        ]),
                    child: TabBarView(
                      children: <Widget>[
                        Container(
                          width: 500.0,
                          child: LoginForm(),
                        ),
                        RegisterForm(),
                      ],
                    )),
              ],
            ),
          )
        ],
      ),
    )));
  }

  setAnimatedContainerHeight(int index) {
    if (index == 0) {
      setState(() {
        _containerHeight = 300;
      });
    } else {
      setState(() {
        _containerHeight = 450;
      });
    }
  }
}

Or using FutureBuilder:

import 'package:flutter/material.dart';
import 'package:travel_agent_app/loginForm.dart';
import 'package:travel_agent_app/registerForm.dart';
import 'package:travel_agent_app/bubble_tab_indicator.dart';

class Login extends StatefulWidget {
  const Login({Key key}) : super(key: key);

  _LoginState createState() => _LoginState();
}

class _LoginState extends State<Login> {
  double _containerHeight = 300;

  @override
  Widget build(BuildContext context) {
    return DefaultTabController(
      length: 2,
      child: FutureBuilder(
        future: Future.delayed(Duration.zero),
        builder: (BuildContext context, AsyncSnapshot snapshot) {
          return Scaffold(
            // ...
            // The context within here is from FutureBuilder, which include DefaultTabController
            // ...
          );
        },
      ),
    );
  }

  setAnimatedContainerHeight(int index) {
    if (index == 0) {
      setState(() {
        _containerHeight = 300;
      });
    } else {
      setState(() {
        _containerHeight = 450;
      });
    }
  }
}