I will be graduating in May 2020 with an BS in Elementary Education and an ESOL endorsement. My dream job is to teach overseas, ideally in the UAE. Is it too early to start applying? ..and will any destinations take fresh graduates?
I actually started my teaching career overseas at an international school. So no, it isn't impossible for you to get a job as a certified teacher overseas as a brand new teacher. However, I think the certified areas of teaching do matter. I'm certified in math and science, which are marketable areas compared to other areas. However, they always look for elementary school teachers, mostly Asia regions including UAE.
I say go for it, just mention that you are about to graduate in May 2020 in your cover letter. Make sure to build teaching aid experience.
Good luck and don't get discouraged if you don't hear back on the first round of job applications.