I am not a teacher.
What is the "I'" all about? There should be no apostrophe after "I" on its own. I thought it was a typo but you've done it twice.
Here, I think you want to say "I'd".
"I'd like to conduct a survey on the employment status of fresh graduates", is the phrase I would prefer.
It does rather depend on the purpose of the survey.
If you want to know whether or not the fresh graduates are employed I would use "status".
If you are looking for information about the general state of affairs (how successful the job hunting is, the difficulties encountered and so on) you could use "situation" but it sounds a bit more vague.
Student or Learner