Please keep in mind that your 20 month old will, eventually, turn into a 3, 4 and 5 year old! I think 18-24 months was the hardest time with my son and my cats. Ultimately, he developed some restraint, and in the meantime, I watched him and them like a hawk. While he is now 4.5 years old, I can tell you it has been a long time since he and they interacted poorly.

Good luck, and please don't give up on your pet. Having pets does so very much for a child's learning/responsibility/humane understanding.