Yes, it is. PBKDF2 derives a DK, a "derived key", which is indistinguishable from random. This is mainly because function within PBKDF2 is HMAC, and HMAC is a PRF. Let's see the definition from Wikipedia:
In cryptography, a pseudorandom function family, abbreviated PRF, is a collection of efficiently-computable functions which emulate a random oracle in the following way: no efficient algorithm can distinguish (with significant advantage) between a function chosen randomly from the PRF family and a random oracle (a function whose outputs are fixed completely at random).
This also means that the bytes of the derived key are independent, even from each other. So that means that as long as separate bytes from the output are used, we can split the DK value into a key and an IV.
Now, fortunately, the scheme provided uses SHA-512 as the underlying hash function. This means that no additional calculations need to be performed if we require 256-bit key material and 128 bit IV material.
If the SHA-256 hash would have been used the PBKDF2 function would require an additional run. Unfortunately, in the scheme above, an attacker would not have to perform such an additional run. This is because the attacker only has to verify the key; it can calculate the IV when it finds the key. So using a smaller hash function requires a lot more operations for the legit user, while not giving any security advantage. This is a bad property for a PBKDF - which unfortunately is present for PBKDF2.
So as long as your key and IV stay below the output size of the hash the scheme above is secure.
If you'd ever required more output than the single hash requires then it is possible to perform additional calculations using a key based key derivation function (KBKDF) such as HKDF. In that case, a good scheme would be:
derivedKey = PBKDF2(password, salt)
key = HKDF(derivedKey, "Key")
iv = HKDF(derivedKey, "IV")
That the scheme is secure doesn't mean that it is optimal. You could think of using a memory hard PBKDF such as scrypt or one of the newer Argon2 variants instead of PBKDF2. You might also have a look at authenticated ciphers such as GCM to add integrity and authenticity to your ciphertext.
Of course, the scheme does depend on the salt being a secure random value. Please make sure this is the case, otherwise, you may end up with a repeating key, IV for identical passwords, destroying security.
A high number of iterations (the "work factor") for PBKDF2 makes it harder to attack relatively weak passwords (and most passwords are relatively weak).