I would have to agree with Shannon. Make sure to take your dog in if it's breathing differently too! Better to be safe then sorry
Oh, and it is important to let your dog have access to as much water as it wants while on this drug, even though it means he/she will be urinating more.
Assuming that your vet has ruled out all other causes of thrombocytopenia and is left with immune-mediated, the the treatment is an immunosuppressive does of steroids to try and dampen the body's response to the platelets. The suggested dose range is 2-4mg/kg and your dog is getting slightly less than the 2mg/kg dose. That being said, there is no research definitely setting the immunosuppressive dose at 2-4mg/kg; it may be higher or lower depending on the animal's response to it and how they metabolize it. It looks like your doctor is starting conservatively. Side effects of steroids include increased drinking, increased urination, panting, weight gain, and increased susceptibility to secondary infections. If you feel that your dog is having trouble breathing, then he/she should be seen. If it is just increased panting, it is a side effect of the drug and not something that would make the doctor take he/she off the drug unless the dog was excessively agitated. I hope this answered your question.