Here is the towel rack I am considering

Bad Idea. How about a hook to the right of the shower door?

A hook is a good idea although there is no room on the right of the shower door as there is a door with the washing machine behind it

Maybe hooks like these?

Can I place the towel bar over the toilet ?

There are hooks that can go over the shower door which work in a pinch.

I have hooks behind the bathroom door for large towels. I was looking for a solution for hand towels

Having the shower door swing toward a metal obstacle is probably not a good idea.

Hand towels, if they are actually used as hand towels and aren't primarily for show, would best be within arm's reach of the sink. The wall beside the toilet might be a possible location, but above it, if the cabinet can be moved, is also possible.

What you need near the shower is a place to hang the towel that you're going to use when you step out of it.

Your hand towel holder should go to the left of your sink -- you don't want it near either the toilet or the shower.

I agree that on the left is better if it is feasible. It looks as if the sink is right next to the door, but the wall to the left could maybe hold either a short towel bar or a towel ring.

I agree with Paul NY and acm. If it is just for a hand towel (pic looks like towel holder is not too big), why not just put it on small wall to the left of your sink ? ......to the left on enterance door?? I woud not put hand towels near shower or above toilet. If I could not put one on the little wall I suggested, I would pick a really nice one..more on the smaller size..(i.e., Turkish cotton) and place it right on top of the counter.

Sorry, but hand towel above toilet or shower area just would look odd to me ;)

Do you already have a towel bar on the wall next to the shower on the opening side of the shower door? That would be the best location to grab as you get out. The wall be the toilet that it opens up to would be very inconvenient and a little unhygienic to hang a towel in my opinion.

Thank you for all the answers, greatly appreciated!!!!