You are totally doing the right thing for the dog and although it is difficult emotionally, you have done the right thing for yourself.
If you want a companion, consider an older rescue cat rather than a bird. Bird cages are an onerous task and cat litter boxes now can be purchased that self clean.
A lot of shelters almost give away their older cats, I paid $5 for my orange cat. Since my felines are indoor, they do not need any more vaccinations. Other than food and litter, there is no other real cost for a cat.
Plus you save an innocent from a life in a cage.
I admire that you gave your dog a better life. I love both cats and dogs and I applaud you for recognizing and loving so much. Kudos Sally.