What can be done to prevent scarring from a burn on my 20-month-old child?

Tips on scar care: In general with any scar that is immature (less than 18 mos old) one should minimize sun exposure and moisturizer the skin daily or more.

Can't once burned: Best is to prevent burn in the first place. Once the burn has occurred you can keep the area clean and moist and avoid infection but the ultimate scarring depends on the depth of the burn. I would see a plastic surgeon to advise in your particular case but usually keeping the burn from drying out and avoid infection then once healed sun protection, moisturizer and maybe pressure or topical silicon.