If you start with a random key and zero counter, there's 128 bits of entropy in the system state. If you start with a random key and random counter value, there's 256 bits of entropy.
Whether that matters depends on what you are using the PRNG output for. If you are using the output for anything where 256 bits of entropy would be an asset – say random 256-bit UUIDs (with some coming from another PRNG instance) – then you could seed the counter with a random value as well. Provided you have sufficient entropy for seeding, of course.
CTR_DRBG in SP 800-90A (pdf) is a ready made PRNG design based on AES CTR with the choices for this kind of thing, as well as key rotation, already sussed out. So you may want to consider using it.