In my opinion, any offer letter that you are required to sign as a "contract" for employment should have a few basic things covered. It should list your status (full time, part time or PRN), should cover your guaranteed base salary when you are called in to work, should detail any benefits that you are entitled to as an employee (insurance, retirement, vacation, PTO, etc...some won't apply if you are hired as PRN), if they have promised you money to keep your license current, pay for conferences or CEUs, provide an annual scrub allowance, etc. that should also be listed.
Remember that this is not a one sided contract meant just to cover the employers rear. It also needs to cover you so that once you start the employer can't pull a bait and switch and completely go back on their word.
Let's think about it in the terms of a lease. You want to rent a two bedroom two bathroom apartment in a newly constructed development near your favorite school district for the kids. The property management company also manages several other apartment complexes in your county. You are shown a GORGEOUS two bed two bath apartment in the new complex and told that you can rent an apartment for $850 a month, just sign on this line. You think, that sounds amazing! It is by the schools I want my kids to attend, it has everything I was looking for and is a steal price wise, so you sign.
Then.....the other shoe falls. You are given a map with directions to another apartment complex in the next town that is located in a different school district. The leasing agent tells you that your new keys will be given to you in the rental office located in the other complex. You go to the complex to find out the development is about 50 years old and in need of substantial repairs. You walk to your new unit to discover that it is a one bedroom one bathroom unit, so you don't have a room for your kids.
You think to yourself, how did this happen?!? They showed me an amazing, new two bed two bath and said I could rent it for $850! You think "I even signed the papers for it!" You go back to the rental agreement and read the fine print you didn't bother to read previously that says that you are not guaranteed a certain apartment, or even a certain complex, you are just guaranteed that you can rent AN apartment for $850 a month and can be sent to any complex that has a vacancy. The property management company fulfilled their end of the contract by renting AN apartment to you, but they did not give YOU any protection in the contract by guaranteeing that it would be in the new development, that it would be a two bed two bath, etc. and now you are STUCK!
If you really wanna work PRN for this agency then tell them you won't sign until your hourly rate is included in the job offer. If they are unwilling to budge, it is probably because they are gonna do something shady down the line. Keep looking around for another agency that won't be so sneaky in their practices.