Encrypt a small amount of data with a password derived from PBKDF2
Is it fine to do that?


Yes, it should be fine, as long as you do not reuse the key/salt-pair for encrypting another piece of data.


  Or is there a more standard construct?


Any authenticated encryption algorithm would work. E.g. AES-GCM with the PBKDF2-derived key.

If you are going to use the same password for encrypting many such pieces of data there are more efficient ways to do it, so that you do not need to compute PBKDF2 anew for each of them. For example, have a constant salt for it and also a message-dependent nonce you use for the encryption algorithm.

There are also alternatives for PBKDF2 that you might prefer, like bcrypt, scrypt, argon2, if you happen to have them available. They make it more difficult to test password guesses, which you might want if you are unsure about the strength of the password.