Unfortunately not, the mainline from London to Weymouth goes through my town of Dorchester (i travel to Weymouth daily). But that's it, there is no line which goes to the coastal parts of Dorset. There is another station in Dorchester which takes you up to Bath, Bristol, but that goes nowhere near Dorset coast. You best bet is Bus.
Portland is easy to reach, but by Bus. Your train will not be close to Portland (your talking a good 3 - 4 miles walk). But yes, I would go via bus from the station.
Places I would recommend - Lyme Regis - which is teaming with fossils down near the cliff, however a huge portion of the cliff collapsed so it might be hard to access.
Lulworth Cove is a another place its a natural made harbour
Durdle Door which is very close to Lulworth
West Bay is another nice place:
And Swanage, which has a Steam Train to take you to Corfe Castle (not pictured)
But as I said, all these places are accessible by Bus, and though you can get to Corfe by train its only to Corfe and back to Swanage.
I'd check the Bus routes, there is a bus to Portland not too far from the train station. However, thinking about it the train you go on stops at Wool which you could easily get a bus from to Lulworth Cove and Durdle Door. Its about 2-3 miles from it.
I would check local buses...try
http://www.dorsetforyou.com/index.jsp?articleid=2183
hope this helps