You can use a global ValueNotifier variable. Then you can change it's content regardless the page in which you are.
Assuming this variable declaration ValueNotifier cartCounterNotifier = ValueNotifier(0);, you can update your AppBar action like this
appBar: AppBar(
    // title and other
    actions: [
      ValueListenableBuilder(
          valueListenable: cartCounterNotifier,
          builder: (context, cartCounter, child) {
            return Stack(
              children: [
                IconButton(
                  icon: Icon(Icons.shopping_cart_rounded),
                  onPressed: () {},
                ),
                Positioned(
                  child: 0 < cartCounter ? Container(
                    decoration: ShapeDecoration(
                      color: Colors.red,
                      shape: CircleBorder(),
                    ),
                    padding: EdgeInsets.all(2.0),
                    child: Text("$cartCounter", style: TextStyle(
                      color: Colors.white,
                    ),),
                  ) : SizedBox(),
                ),
              ],
            );
          }
      )
    ],
  ),
Update: 
So to update your action button, simply change the content of your variable like this
cartCounterNotifier.value = cartCounterNotifier.value + 1; // or another value