Whether you like 'em or not, down dogs are like the bread and butter of any yoga practice, from vinyasa to ashtanga. Which is why it is so important to do them correctly (gut pulled in, looking at your hamstrings). It is also crucial to flow into the down dog with ease.
Watch this video to learn a flow sequence that'll move you gradually into a down dog. Try this chest and shoulder opening flow before coming into your early morning Down Dog.