Update dartdoc to v0.18.1 and fix API readme (#16080)

* Update dartdoc to v0.18.1 and fix API readme, borrowing from docs.flutter.io
diff --git a/dev/docs/README.md b/dev/docs/README.md
index 88a7221..0b3691b 100644
--- a/dev/docs/README.md
+++ b/dev/docs/README.md
@@ -1,4 +1,11 @@
-This directory contains the documentation generator for
-<https://docs.flutter.io/>. Those docs are updated only for the beta
-branch, see <../bots/docs.sh>. You can find docs for the master branch
-staged at <https://master-docs-flutter-io.firebaseapp.com/>.
+Flutter is Google’s mobile UI framework for crafting high-quality native
+interfaces on iOS and Android in record time. Flutter works with existing code,
+is used by developers and organizations around the world, and is free and open
+source.
+
+### Documentation
+
+* **Main site: [flutter.io]()**
+* [Install](https://flutter.io/setup/)
+* [Get started](https://flutter.io/getting-started/)
+* [Contribute](CONTRIBUTING.md)