Maybe I missed something, but you didn't mention how old your child is, what testing you are considering having done and the reason you want the testing done... depending on the answers to those questions you will likely get difference responses.
At the extreme of reasons you have some parents that want to test simply because they want to reassure themselves that their child is special... Those parents will often shop their kids around to be tested over and over until they get a score that they believe fits their expectation, might sound crazy but it happens.
Other parents have noticed things about their child and want to make sure everything is fine and to see if he/she could use a more advanced learning environment than they currently have... No one knows what reason you have for looking at having your child tested... hopefully it is for the right reasons and not the wrong ones.
As for your concern that a psychologist is going to give you a better result than a grad student... Maybe yes, maybe no... some psychologists don't spend as much time or effort in testing as they should, some grad students take it more seriously than psychologists... your child might also be impacted by who the tester is.. they might respond better to a male than a female, maybe it is reversed... maybe they respond better to someone that looks younger like the grad student or maybe better to the older person that reminds them of a grandparent.. there are a lot of factors and none of the answers you get here are going to be able to factor in information about how your child interacts as you will be able to.
As for the type of test you are having done, if it is for placement in a gifted program then you need to find out the tests that are acceptable, if it is just for your own piece of mind then there are other less expensive tests that will placate your fears but likely wouldn't be accepted for placement, but again I have no idea what your reason for looking into testing is.
