Can I build a deck this low to the ground?
Sure, you can do that.  Rather than using a beam though, just use some of those pre-cast concrete pier blocks (like in this article).

If you really want to use a beam instead (it might be cheaper) you'll want to make sure the treated wood you use is rated for ground contact.  You might have a hard time finding ground-contact rated 2x6's at a local home store, but they probably do carry ground-contact rated 4x6's that you could use instead.

Another option would be to use railroad ties for your "beam".  just dig a trench, fill it with gravel, level it out, compact it, and set the railroad ties on top (note - railroad ties are much heavier than they look).