This is an accepted solution.
at the moment Dawn doesn't implement any cart drawer. The only option as you noticed is to link to the cart page.
I also don't see this feature in the Shopify Dawn Roadmap at the moment.
There was a request for a Cart Drawer that you can vote up (don't know if it will help)
You can also try out HypeCart which is a cart drawer that also includes the option to provide great upsells and cross sells both in the cart and after the checkout.
It works great with Dawn!
You can find it here: https://apps.shopify.com/hypecart