Is it OK to use a secret IV as key when creating keyed MD5 checksum for fixed-size data? Is it OK to use a secret IV as key when creating keyed MD5 checksum for fixed-size data?

Because data size is known, attacker cannot append anything. And I think it's hard to raise chosen-plaintext attack if the secret is well kept, but I’ld like to be sure.
So the idea is to use the IV of MD5 as a key to create a MAC. Like CodesInChaos mentions in a comment, it would be pretty much equivalent to using $H(k||m)$, if your IV is randomly chosen.

By only using it on fixed length messages you avoid the length extension attack, but that is not the only attack on hash constructions that try to create a MAC. In this question on $H(k||m||k)$ the answer provides links to an attack that uses internal collisions (pdf, Proposition 4):


  This means that an attacker can replace or delete $w \le s$ trailing blocks, and that the attack is applicable even if the input is of fixed length [...]


It can also be applied here. So, no, it would not be secure. At least strictly speaking: the attack requires seeing $2^{n/2}$ authenticated messages, though a smaller amount could allow an attack with some probability.

You should use HMAC or another standard MAC instead. I would also consider a more secure hash than MD5, if you use a hash based MAC, even though the attacks known for MD5 are not sufficient to break HMAC.