Yes GDP is a good measure of the prosperity of the average person.
Explanation:
GDP - Gross domestic Product
The GDP will take the entire output of goods and services produced in a year by everyone within the country's borders.
- Real GDP is the best than nominal GDP
- GDP acts as a component of a human welfare
One drawback of GDP is it does not take the amount of pollution, safety and health. It does not take "well-being" too. Suppose if everyone starts working on weekends without "leisure", "GDP" does not take into account. So now it fails to check prosperity along with well being of the average person.
