Why not wait until you are IN? MEASURE? A shelf above a tension rod seems unnecessary, and room to hang with no drag on counter top seems a better idea. You can get a tension rod overnight, from Amazon: )

You have cabinets.....what is the need to junk up a shelf with doo dads. Move IN.

I agree wait but why not something that folds out of the way when not needed .

Do not use a tension rod (like a shower curtain rod). They are not designed to hold continous weight of clothes. Either a wood rod cut to length with screwed to the wall hangers or a steel rod, cut to length or two piece extendable. Shelf above or not, just depends if you think it will be used.

Make the rod high enough that full length dresses or other items can be hung to dry without touching anything else.

The room seems quite dark. Maybe think about adding under cabinet lights, an diffused LED light strip on the top of the cabinets to provide reflected light above the cabinets (use a dimmer), etc. Just being brighter will make the room feel less depressing.

I'd put a strong rod in but skip the shelf. Too cluttered and not needed with your cabinets.

I agree with what luna and babe said about the strong rod. It will be very handy hanging things from the washer or dryer. As you have already moved in, you can figure out ahead of time before the appliances arrive any scheme you want to have in the room. I would not rule out a shelf with the rod as part of it's design; it is a laundry room after all and better to store some excess things there than in other areas of your home. I can tell by the design of your LR it is a nice home and you will know when too much is too much,

I’ve been using a tension rod for over a decade and it is fine for everyday use. We wear a lot of high tech fabrics and of course my husband likes his fancy pants undies that can’t go in the dryer. We actually have 2 drying racks plus the tension rod, some of my jeans that have a lot of stretch in them go on a drying rack.

You have a good idea with the rod and shelf, you can get a set like your photo or I'd probably go with separate pieces in white. You can add color decor on the shelf to coordinate with a rug and the rest of the room. Just be sure to check your rod and shelf measurements, the shelf depth shouldn't block the lighting above, and the rod depth should be hold a coat hanger which needs 24". Also consider the height of the rod - you want to be able to reach above to hang clothes comfortably and still allow space at the bottom so you aren't accidently sweeping items off the countertop.

The tile would be pretty or you can hang artwork for the days when nothing is hanging on the rod.