ShakaZulu
Contributor
I dived Dos Ojos last year and there was a fairly novice diver with us. The main issues for a new diver in a cavern are air consumption and buoyancy control. If you run low on air, you have no direct access to the surface. Sure, your buddy or guide can share air with you, but it's not so much fun going through dark tight spaces side by side. If your buoyancy is not so good, it takes a minute to silt up the cavern.
I'd say do a few dives in Cozumel and see how your air consumption and buoyancy is. Ask your dive guide if he/she thinks your skills are adequate to dive the Cenotes. If so, you can just do a day trip to the mainland (no need to stay overnight). Your dive operator in Cozumel should be able to set everything up for you with a day's notice.
Have fun in Cozumel!
They will always say yes....and so continues the destruction of the cenotes