Couple of comments: Check the road from Zeehan to Corinna - it MAY be 4WD, and involves crossing the Pieman River ([-]ferry[/-] barge) -
see here for schedule and charges. Then, the road from Corinna to Arthurs River is the Western Explorer Road.
See here for a description. Personally, I wouldn't take my own sedan car on that road. If you are hiring a car, you may not be able to take it on the WER, due to unsealed parts (over 200km). I would only suggest that route for a '4WD adventure' type trip. Even if you can do it in your hire car for your 2 week trip it'll take a disproportionate amount of time.
Furthermore: there are major bush fires burning between Marrawah and Corinna at the moment.
See here, then zoom the NW coast area. Should be under control by March, but roads may still be closed due to possibility of falling burnt trees. See
TasAlert map.
Personally, in spite of the 'NW Coast' cheerleaders, I still would go from Zeehan through Tullah to Cradle Mountain; that would clip 2 or 3 days off. There are fires east of the Cradle Mountain region, but not impacting the Dove Lake / Lodge area.
Remember roads in Tas are usually winding and narrow; anywhere you want to go will take a bit longer than you think, especially on the west coast.
Without the northern west and NW Coast part, your itinerary is do-able in the time. If you really want to go to that part of Tas, omit the remote west and NW coast in this trip (but keep the west coast Strahan and Zeehan etc) and do it in a 4WD on a separate trip. That opens up a whole bunch of other interesting places, such as Trial Harbour, Granville Harbour
and the old mining towns and tramways now off the highway.