[KyleGoetz]

It's correct, but it sounds slightly colloquial because you didn't add が after 日本語.

Explaining the difference between わかる and しる for "to know" is not very easy, but a general rule of thumb is that if you can substitute "understand" for "know" without getting a weird sentence, it's わかる. わかる is more knowing concepts and しる is more knowing facts.

Do you know Japanese? わかる
Do you know the word for "tomboy" in Japanese? しる

Also, Japanese people use pronouns a lot less than we do. Compounded with that is using あなた is pretty rare. You should, instead, say 〜さんは... instead of あなたは when speaking with someone, where 〜 is his name.