You could drive up to New Brunswick from Portland, or you could take the CAT from Portland or Bar Harbor (next to Acadia) into Nova Scotia, and then drive.
Only if your destination is NS.
A couple of comments. NS has enough to keep you occupied for 1 week without stopping in NB or PEI. If you choose NS, then the CAT Ferry mentioned previously is a very good, albeit expensive, option. There is another thread in this forum discussing vacationing in NS.
Although you can spend a week in NB, it is much better suited to combine with PEI, especially given your desire to spend a day or two on the beach. your route up from Portland (3-4 hours from the Canadian border) would take you through St Stephen (Ganong Chocolate factory), St Andrews (Algonquin Hotel), St John (Reversing Falls mentioned previously). Heading on towards PEI you would have the opportunity to do some hiking in Fundy National Park as well as some kayaking. It is very fun to do the later around Hopewell rocks, only to come back at 6 hours later and walk in the exact same location where there had been 20 feet of water. Moncton doesn't have any other claim to fame other than Magnetic Hill (not worth it IMHO).
PEI is awesome, great for golf, walking/lounging on the beach. It is very busy during the summer, with most of the crowds congregating in the Cavendish area (home of Anne of Green Gable). There are many nice beaches here although you can find equivalent in other parts of the island which are much less populated. The other prime tourist spot is Charletown (spp?), the only city (pop 30,000!) on the island. BTW, you only pay for the bridge ($35-$38 CAD?) on the return trip. It is much more enjoyable from a bigger vehicle as this allows you to see over the sides of the bridge.
Drive times.
Portland-Border/St Stephen: 3-4 hours...could run into moderate lines at the border...there is an alternative border crossing only a mile upriver which never has any line-ups. St Andrews is about 1/2 hour away, albeit a bit off the track to St John.
St Stephen-St John: 1.5 hours.
St John-Funday National Park: 1-1.5 hours
Fundy National Park-Moncton: 45 minutes-1 hour.
Moncton-PEI Bridge: 1.5 hours.
PEI Bridge-Cavendish. 30 minutes NW. PEI is so small that you are never more than 1 hour or so from all of the prime tourist destination, unless you you to the eastern or NW tip of the island (not bad if you don't want the tourists)
I liked St. John better (vs Fredericton), its smaller and prettier.
Funny assesment. Actually St John is about 115,000; Fredericton about 45,000. IMHO, St John has a much grittier feel to it with the oil refinery and the frequent summer fog while Fredericton is much cleaner with the greens on either side of the river. That being said, Fredericton would be a bit (1-1.5 hours) out of a Portland-PEI road trip and you can easily spend a day in St John...
Hope this helps.