My django application has become painfully slow on the production. Probably it is due to some complex or unindexed queries.
Is there any django-ish way to profile my application?
Try the Django Debug Toolbar. It will show you what queries are executed on each page and how much time they take. It's a really useful, powerful and easy to use tool.
Also, read recommendations about Django performance in Database access optimization from the documentation.
And Django performance tips by Jacob Kaplan-Moss.