Your translation is perfect, but I think て is not indicating purpose. It rather means method.

More verbatim translation is:

By using what kind of books do you study Japanese?

"By" at the top of the sentence comes from て-form.

Related dictionary entry (quoted from デジタル大辞泉):

［接助］活用語の連用形に付く。ガ・ナ・バ・マ行の五段活用動詞の音便形に付く場合は「で」となる。形容詞、形容詞型助動詞に付く場合は「って」の形をとることもある。

 

手段・方法を表す。「歩い―通学する」「泣い―抗議する」

In this sentence the purpose is to study Japanese but not to use books. So you can use のに (that indeed means purpose) to say the same as follows:

日本語を勉強するのにどんな本を使っていますか。

Your translation is perfect, but I think て is not indicating purpose. It rather means method.

More verbatim translation is:

By using what kind of books do you study Japanese?

"By" at the top of the sentence comes from て-form.

Related dictionary entry (quoted from デジタル大辞泉):

［接助］活用語の連用形に付く。ガ・ナ・バ・マ行の五段活用動詞の音便形に付く場合は「で」となる。形容詞、形容詞型助動詞に付く場合は「って」の形をとることもある。

手段・方法を表す。「歩い―通学する」「泣い―抗議する」

In this sentence the purpose is to study Japanese but not to use books. So you can use のに (that indeed means purpose) to say the same as follows:

日本語を勉強するのにどんな本を使っていますか。