Answer: Varicella (chickenpox)
Explanation:
The illness prevented by proper vaccination that the toddler has is Varicella (chickenpox).
Varicella is a very contagious viral infection which causes itchy, rashes on the skin. Other symptoms include headache, fever, tiredness, loss of appetite etc.
It can be spread when the person coughs or sneezes, through kissing, skin-to-skin contact, during pregnancy etc.