How soon can I get a transfer to another unit in army national guard?

Transferring from the ARNG is a lengthy process but not impossible. However, the beauty of the Reserve elements is they really do have to adapt to your civilian circumstances wherever they may take you.
First step is find a recruiter. I would suggest going USAR as transferring units in the Reserves is relatively easy. If that works for you, any non-ARNG Recruiting station should be able to help.
If you want to go Iowa NG, you'll need a Iowa NG recruiter.
With either recruiter you'll complete a DA 368, conditional release, which wool travel up the Ohio NG CoC for approval. That's the lengthy part. Once approved, the recruiter will find you a new home.
Good luck. Stay on top of your Ohio NG S-1.

The guard can not keep you from moving. However, because you contracted with Ohio they can keep you on their books - so you would be responsible for attending training with them. The state of Ohio is paying for your training so they may not want to give you up right away. It is possible to request a conditional release in order to move to another unit (in Iowa). You will need to work with retention/recruiting to find a unit and slot for your MOS.

Are you split training or are you in your AIT already? Anyway, after you complete, you need to talk to your Readiness NCO at your unit. His job will be to determine if you are able to transfer administratively, no flags or adverse actions pending, then send you information to the Interstate Transfer Coordinator at your State Headquarters. That person's job it to coordinate with the IST in the gaining state to find a slot in the state for your MOS. If you already know where you are going to live, I would also suggest that you contact the local NG recruiter about available slots in the area. If you can point the IST's towards a unit that is willing to accept you, it can speed things up a bit.
People that tell you about how hard it is to transfer just didn't ask about how it was supposed to work. I have attached a link that lays out what I have told you above in more detail. https://www.nationalguard.com/how-to-transfer-to-another-state