Littlemaps:
I think you are right, you will have better luck closer to your move date, but that adds stress. From my experiance your biggest challange will be to convince the landlord that you can cover the rent (ie you are working), and finding a place that will take a dog.
Going through a letting agent is not the only approach, and you will have a tough time getting interest from the bigger ones. Just my opinion but I think you need to decide where you going to be and focus your efforts. If Plymouth (Torpoint) is the place it is big enough to offer a variety of rental accomodations. Plymouth has a big student population so there are lots of 'rooms' if that is what you are after. (I travel through Devon and Cornwall on business)
I am in Exeter, about 45min drive from Plymouth and there is (usually) lots of choice here as well.
Not sure what your situation and Cornwall is a lovely place, but unless your are looking for tourism or hospitality related work you may find it tough. You may be better off in a larger center (like Exeter) where there are more opportunities, and then move to your dream location when you are more established.
If you are looking for a room try
www.spareroom.co.uk . This site is usually private landlords or homeowners who are renting a room.
Let me know if I can help.
SW1392