Hyperdia

Hi,
Yes, it exists. The station you are looking for is Miyajimaguchi. It is a bit less than 30 minutes from Hiroshima Stn.

You can see both Hiroshima and Miyajima with an early morning start. You can cover the Peace Park/Museum, castle, Shukkeien Garden and Okonomiyaki-mura, and then go down to take the JR ferry to the island. Aside from the Itsukushima Shrine with the giant "floating" torii, the Daishoin Temple is also a must-see place. There are several other pagodas and temples, and climbing Mt. Misen offers a fantastic view over the island and whole area.

If you have time, just a bit past Miyajima is Iwakuni with its iconic historical bridge and mountaintop castle.

Good luck.