Is this workout a good start for the 3000m steeplechase event?

I think doing the first lap without and second lap with is better. Also, you could just do the first part of the workout normally and the last 2-3 reps (depending on the workout) with hurdles so you can practice being tired and hurdling. If you know how to hurdle already then the next step is to get comfortable navigating the hurdles while tired.

If you even tempo on the track, you could put 2 or 3 hurdles around the track and do the last mile of your tempo over hurdles so you can practice having your rhythm broken up while running moderately hard.

Just don't overdo the hurdle workouts. It's good to get flexible and practice, but too much could cause some overuse injuries more quickly. And steeple chase is about fitness first, hurdling second.

If you have a goal of 9:30 steeple you may want to work on your 3k speed. Generally, people with really good hurdle ability can run about 40 sec slower than that flat 3k ability or around your 2 mile time.