IMO the rustic./primitive linens shown in this vignette are appropriate with the rustic style of the set. You can always add colorful toss pillows if you like

What's not working is the paint color for your walls. The neutral color is too yellow to complement this set that leans towards gray and the dark teal is just, well...........bad IMO.

If you want to add some color, do it with wall decor, window treatment and accessories.

Well first of all what sweet rascals you have there! I too have a dog but I use a folded quilt that is easily washable at the foot of my bed over my white duvet. Do you think that would work? Are the paint colors newly painted and something you chose or are they colors that were already in the home?

Because the furniture itself has so much movement within the grains of the wood I think keeping pattern to a minimum is likely your best bet. That said I would bring in texture. I will pull some ideas for you brb

This is the quilt I have folded at the foot of my bed which my dog is free to lie on. It washes up well and Ive had it for 7 years!

It saves my white duvet which I wash and bleach with no issue. I love the linen texture. It is from PB and comes in several colors but in your case I would do the natural linen color. Here it is on my bed in the blue