In my experience, dogs do very well with both carboplatin and doxorubicin. They do need regular bloodwork to make sure they can handle the next treatment, and sometimes have to skip a week and go on antibiotics if their white blood cell count gets too low. Most of them don't even realize they're getting chemotherapy.
Doxorubicin can cause stomach upset, and is cardiotoxic. The cardiotoxicity is cumulative, and the risk is greatly lessened when a combination therapy is used. If your oncologist hasn't already mentioned it, it's best to have a baseline cardiology workup before starting doxorubicin therapy. One of my patients last summer was on weekly doxorubicin therapy, and she did very well for a number of months.
I like carboplatin better than its related drug, cisplatin. Though it is more expensive, carboplatin is much less toxic to the kidneys and does not have to be infused over a whole day with diuresis like cisplatin.