Something Stephen Breyer said on Colbert: "My father's advice to me was: whatever you do, stay on the payroll"

That said, if you're in a position to move sooner, and you feel your comfortable with the procedure, eliminating the wait will help eliminate the worry that goes with the wait.
The question is, how will that impact you after?
And yeah, COBRA is usually available if you lose your job, but it's almost never subsidized by the employer, meaning the monthly cost can be prohibitive. The ACA is available, and seems to have good coverage, just not sure where some of those policies stand on trans related coverages. Will vary considerably by state and provider.