(Generic) Terbutaline Sulfate helps relax the airways to make breathing easier for dogs and cats. Terbutaline Sulfate is most commonly used in the treatment of bronchial disease, including asthma and allergic bronchitis. The typical dosage for dogs is 1.25-5 mg per lb. body weight three times daily. The typical dosage for cats is 0.05-0.1 mg per lb. body weight twice daily. Terbutaline Sulfate.