Hello,
Ideally, you should get disability and life insurance as early as you can. While you are young and healthy you can get very good deals. As age creeps up on you, the premiums get higher and the benefits lower. Also you should think prospectively and provide for yourself enough to sustain a good standard of living.
The catch is that while you are making a beginner's income, it will be hard to buy much insurance, because insurance companies will object to your buying a policy for more than you earn now. However, as your income increases, your age will also increase, and additional insurance will be more expensive to buy, unless you have a policy rider that allows for increases in value at the same price.
Another catch is that you may buy something decent now, but as inflation increases, your disability insurance becomes less than adequate, and then again, buying more insurance will be more expensive, because you will be older.
If you buy enough insurance, at the beginning it will look like excessive, but as time goes by, you will be happy you did.
Another thing is that, while you are young, it makes sense to buy some "whole life" insurance, even if it is a small amount, because it will increase in value on its own over the years. The agents will try to convince you to buy other kinds, such as "universal life" or whatever their product is called, because "whole life" is not as profitable for the insurance company.
Greetings.