Yes, you can :)

Yes, using "why don't we..." is making a suggestion. If someone has a better idea, they would be free to give their suggestion. "Why don't we rest a while, then we can both cook our dinner together?" "Why don't you go to the store and buy some vegetables?" Or a suggestion that will make you happier...."Why don't you go read a book while I take a nap?" Why don't you stop talking so much and give my ears a rest!"

I think why don't you is a great verbal tool for complaints Why don't you take your golf clubs and shove them right up... If you love your car so much, why don't you marry it? Why don't you go jump off a... Why don't you think next time before you open your %^&% mouth?

Yes it sounds perfect to me :-)