It looks like if you did a rug it would most likely need to be big enough to cover that whole area. The small rug would have to be taken away.

8 x 10 would be best, but turn this one the other way before you buy a new one, or turn the table. 9 x 12 is going to be too big. I have a 13 x 13 dining room and it has an 8 x 10 rug. To be honest, if I had to do over, I'd get a round table!

Without seeing your space, it sounds like your dining room isn't really "a large expanse." It might be possible to break up the floor with interesting furniture and/or colorful upholstered dining chairs. It might also help to make the room feel larger to omit the rug. When I replaced the carpet in my dining room with LVP, it seemed to silly to put a rug down and I do not miss one.

The room is coming along very well. Definitely take your time to do it right. . Are there any rug stores in your area? Especially one that might be independently owned. Often, they have a back room of rug remnants that you can purchase and they will size it and bind it for you. There is one in my area that does binding for $2/linear foot. And you don't even have to have purchased the remnant from them. You may be able to find a sisal or textured piece that fits your need as a remnant and have it cut to size. Is there a Habitat ReStore in your area? In my area, new carpet remnants are always being donated by stores. I got a new 15x15 textured remnant for $25 (had to wait and wait for the markdowns), had it cut and bound at a local rug store for $88. Sweet! Coincidentally, the rug store had donated it to Habitat when they cleared out their warehouse when the building was sold. The carpet style was still in stock and was $12/sq ft .if I had bought it from them directly. I love a bargain!!!! When you want a bargain you do have to be willing to wait for what you want and/or be flexible to know that maybe what your heart is set on is not the best thing. Stay open to possibilities. Sisal is sold by the sq. ft at rug stores.You could have an area rug made. It might get pricey but wait for a sale or maybe find a remnant. Here's a sisal wool I splurged on at the same rug store after my bargain rug. Lots of colorways available for sisal if you go that route. Also, delivery fees have gone crazy where I am so look for ways to save on that if you go local. The two rugs were far too large for my SUV so a friend and I rented a large van for $55 vs. the $175 delivery fee and brought it home ourselves.