I have taken a few pics of Durdle Door and Bat's Head earlier in the year. As well as having other conditions right i.e. the weather, the way the light sets and reflects to give detail on Durdle Door is best around April and October, so September is probably a fairly good time to go.
To endorse what others have already said, depending on where you want to take your shots from, either the beach or from the cliff, the steepest section is from the cliff to the beach and back. Having said that, it is a 'maintained' set of rough steps.
If you aim to take the shots from the beach, make sure you have checked the tides for that day.
Durdle Door from the cliff
Durdle Door from west to east. The shadows on Durdle Door can sometimes be lit from the low sun on the white cliffs.
Durdle Door Sunset
Bats Head and Bats Hole
The light can be great towards sunset and just after and I hope to return to Mupe Bay which is the other side of Lulworth, which is even harder to get to due to the army firing range for a sunrise and sunset.
The main thing missing for me in my shots was an angry or more dramatic sky, but without the rain. As you are literally in the middle of nowhere, if the weather changes you won't find shelter in a hurry. I was out walking the coast for the day but waited at Durdle Door for the sunset along with half a dozen other togs on a beautiful February evening.
Good luck.
Jas