Is it possible to rotate the toilet ?

It would be a little challenge and potentially a little costly, but it it's possible, swap the sides of the sink and the toilet and turn the toilet 90 degrees so the back is against the back wall. You don't need as much headroom above the sink because you don't stand directly in the sink, but facing it. It would require moving plumbing around a good bit and might not be worth it to you, but I think it's the only arrangement that would make it usable.
My Mom had a tiny powder room that was similar and her toilet was against the taller wall facing the door with the sink on the shorter wall with a very small piece of art above it in lieu of a mirror. It was still tiny, but it was charming and served the purpose.

All good advice on swapping walls! Right now you can use this as a conversation piece, "What were they thinking?"

Rotate the toilet and wall floating sink, like "A Kitchen....'

Yep, agree, the toilet needs to move to the other wall.

Ideally move both the sink and the toilet to the back wall. Sink on the left, toilet on the right.

Here are a few ideas!

There are tiny wall-mounted sinks for hand washing that may help.

I really like Keitha's idea...

Terrific ideas! Thank you sooooo much! I'll be posting more. House a bit of a design challenge!

Here's a tiny powder room I did under a staircase. Toilet was under the sloping wall and we used a corner sink, as you can see, with a mirror cut in a mountain shape to go up the two corner walls.
Carolyn Albert-Kincl, ASID

We just remodeled our Adirondack log cabin's @ 5' x 7' bathroom with a layout like yours. The cabin is Adirondack Great Camp style. Believe me, I spent hours and hours measuring everything down to the half inch and researching options.

Put the toilet where the sink is or consider a new corner toilet (they have a triangular tank) where your wood shelf hangs. If you want to spend alot of money, consider one of the new "tankless" toilets. (The price stopped me in my tracks.)

We installed the sink where your toilet is using a white vessel sink on top of an 1800's cherry washstand. The washstand is 18" square and because the legs are thin, gives an open feeling. Plus it has a shelf for storage. You can find washstands on ebay or at antique stores. Ebay often has cute shabby chic french metal washstands. (You could even use an antique plant stand.) They also have vessel sinks in all colors of art glass and price ranges.

Another option is a new or vintage wall hung corner sink.

We installed an all glass shower to keep the open feeling. For towel storage I hung pack baskets on the wall. For sundries, I hung a creel basket next to the sink. Everyone loves the look and says how large the bathroom looks now (as I laugh).

You mean; the last owner didn't think!
Do you think you can switch the position of the toilet, if not then you might want to remove the sink and replace it with a corner one, or move the existing one down towards the door. [houzz=][houzz=][houzz=][houzz=]

Remove the door and replace it with a barn style door. (see photo above)

I don't know if this charming door would fit into your plan but LOVE IT! Very similar to the one Carolyn did.

I thought to move the sink away for the toilet if there is room. Then you just add drama to the room like Carolyn showed or a beautiful half way custom tile like glass or something dramatic. The yellow bathroom above is pretty. I love the copper look.

The nice thing about a powder room door that opens outwards is that it will always remain closed if it's in a hallway.

If moving things isn't an option, how bout a smaller sink? And put a nice tile or wallpaper behind it to play up the powder room
http://www.getprice.com.au/RAK-Bathware-Compact-Slim-Wall-Basin-Tap-Hole-Yes-RHS-Sinks-Basins-Gpnc_630--83477222.htm

Here's a nicer looking one
http://www.homeportfolio.com/catalog/Product.jhtml?prodId=178364

Our tiny powder room is under the stairs (6'X3.5'), like the photo above but it does work functionally. The pedestal sink has the pedestal closer to the wall than this photo. Due to water damage, the room is being remodeled. The floor will be the slate that's in the rest of the downstairs (dark brown primarily) and the walls the soft beige of the rest of the down stairs. My problem is the decorating of this small space. Rectangle mirror? Shelf for towels and tp? Pictures in the room?

A powder room is one place where you can use a lot of color, so I wouldn't go for beige, but for a color you love but are afraid to use. If there's space, by all means use art, and sometimes you can use really big art in a small room. Maybe run mirror on the entire wall where the pedestal sink is going. The glass people can make the cuts around the plumbing. But try not to reflect the toilet. Maybe use a chair rail and mirror the entire room above the rail.

The least cost of moving plumbing for sink or toilet, is the sink. I would move the sink to the left corner or purchase a new corner sink.