Whether it is down drive sized is highly unlikely as the real trend for down drive just really kicked in over the past year, and that looks like an older model. You should remove the wheel from your bike and see if the side opposite where your freewheel is on (so the left side) has threads anywhere. Perhaps it is a washer covering the threads?
Probably not though.
That means, your rear wheel uses standard freewheels which only go down to 16 teeth at the smallest.
Your options: Get a new hub. - Either cassette, or down drive (cassette, generally, is better), and build it up into your wheel. You may need new spokes to do so.