Clicking sound coming from rear
If you have a one month old bike bought new you should be able to take it to the shop you bought it from for a free drivetrain and brake tune up, and to address problems like these that crop up in the first few weeks of ownership.

The click is very loud and occurring at low speed. It does not sound like the indexing being off a little. It sounds like the chain in catching on something  but I cannot see it moving on the smallest sprocket so it's not trying to jump to the next largest sprocket.

I'd look to see if the chain in catching on something around the derailleur cage. 

Check that the wheel is seated in the dropouts properly. If the wheel shifted significantly the sprockets will not be parallel to the derailleur cage. Another possibility is that the derailleur hanger has been bent which will also misalign the sprockets and derailleur cage.