I recommend the school you got your CFI at for a bit. The reason I say this is there are still quite a few CFIs out there competing for jobs. You are a LOT more competitive with a few hundred hours of dual given as opposed to the wet CFI. Most schools like to hire their own first, then hire outside. Usually there isnt too much of a shortage to hire their own. Most schools if they hire outside are training academies and they want 100-200 hours dual given first OR a pat 61 school who wants a lifer.
Fortunately, the airlines have been hiring some of those CFIs who have 1000+ hours of dual given so the slack is starting to get picked up. Good luck on the CFI oral!