"He has been drinking beer since he was nine."
Translation:Pije pivo od svých devíti let.
Yes, your translation is fine. Czech is quite free with its word order. I would say the variant without "už" is closer to the English sentence.
One thing, though: Your sentence can mean two things without context. It can also mean "He has been drinking beer since nine o'clock". If you include either "svých" or "let" (or both) in your sentence, the meaning will be clear.