OMG - great idea! I went myself about 4 years ago, and had a blast. I drove out with a friend, and we took the ferry over to Argentia, and drove 9000km around the island, and left by ferry from Port aux Pasque. It was honestly one of the best trips of my life!!
I think the best time of year would be late June through late August. I say late June because a lot of the spring time foliage and flowers were long gone by the time we showed up in late July (we were on the island for 2 weeks solid). Also you will see many more icebergs earlier in the summer (although they are lasting later in the summer each year) We saw loads of whales, and our share of icebergs, and had a heat wave too!!
In August - think the first long weekend - is the George Street Festival. Also - following Wed (think) is the Regatta. 2 VERY long standing traditions and good times.
We stopped contstantly along the way but our general route was headed to Trinity/Bonadventure, then up to Bonavista, then to Grand Falls-Windsor (Gander), then to Twillingate, then up to L'anse aux Meadow and St. Anthony (please do not miss the northern pennisula - it is the best!!) back down to Cornerbrook, Stephenville, Rocky Harbour, Gros Morne (yes we climbed it too!), Codroy, Rose Blanche, and then headed out from Port aux Basque. The accents are as varied as the landscape!!!
Only after getting back to Cape Breton did we do the Cabot trail, and I am so sorry to say - it was a big let down after all we had seen and done on Newfoundland. We should have done it before heading over. Don't get me wrong - I'm coming to NS soon and will have loads of fun there too.
If you need any info - places to stay or specific things to do - drop me a line. :o)