Upgrade dartdoc to 0.11.0 (#9805)

diff --git a/dev/bots/docs.sh b/dev/bots/docs.sh
index e9fc10e..952dc3c 100755
--- a/dev/bots/docs.sh
+++ b/dev/bots/docs.sh
@@ -2,7 +2,7 @@
 set -e
 
 # Install dartdoc.
-pub global activate dartdoc 0.9.11
+pub global activate dartdoc 0.11.0
 
 # This script generates a unified doc set, and creates
 # a custom index.html, placing everything into dev/docs/doc
diff --git a/dev/tools/dartdoc.dart b/dev/tools/dartdoc.dart
index 76ed5ac..e0ea582 100644
--- a/dev/tools/dartdoc.dart
+++ b/dev/tools/dartdoc.dart
@@ -77,7 +77,9 @@
     '--footer', 'lib/footer.html',
     '--exclude', 'temp_doc',
     '--favicon=favicon.ico',
-    '--use-categories'
+    '--use-categories',
+    '--category-order',
+    'flutter,Dart Core,flutter_markdown,flutter_test,flutter_driver',
   ];
 
   for (String libraryRef in libraryRefs(diskPath: true)) {