We did it for 4 summers in our Cal 46, So had at least 3 months in AK each year. We did most of it (in two stages in C Dory).
I would say a trip or trips, not to be missed! Definitely you want heat, and you want full camper canvas. I would say a dinghy is also on the list of essentials. Although it can be done in a month, I would feel that at least 2 months is preferable--and 3 if you can do it!
No reason not to do it in the Angler--you have the bunks, and can heat the cabin. Consider that the water as well as the air will be cold. It will be in the 50's, and in places like Glacier Bay, Tracy Arm, it will be lower--in the 40's. Air temps will be in the 50's--maybe 60's, but can be in the 40's, and we have seen night temps in the 30's during the summer.--more in the high 40's.
Lots of places not to be missed. An option is to tow the boat by land to Prince Rupert, from there you can explore upper BC coast out to the queen Charlottes, (not to be missed--and I don't see a lot of folks going out there among the C Brats). It is only a few miles to AK, from Prince Rupert.
I would have a kicker, if you don't have twins, or have a dinghy motor which would double. You want to equip the boat with spares to be sure that the trip is safe and comfortable. We happen to feel that an EPRIB or PLB is a good safety feature. A portable hand held water proof VHF is good. Currently I would also have an AIS receiver, but not essential. Radar is not essential, but nice to have, some days.
Rarely did we see weather where a C Dory could not move. There can be days of rain, or days of overcast, mist and fog, so be prepared. On the other hand, we had some trips where rain and fog were the exception. Often you want to plan around the weather, and where you need to voyage.
Guide books by Don Douglas, Renee Hemmingway, are dated (1995 and 1999) but still full of great information. Fine Edge Publications, has about everything you need, just select what you want!
:
http://www.fineedge.com/index.html
The Waggoners Cruising guide 2015, updated yearly is a great place to start. When we first started cruising, I was able to get a complete set of charts from a friend who is a tug boat skipper, and there were over 200 full sized charts. Today with a good chart plotter, and two of the Fine Edge Atlas, you have the entire trip covered.
Go for it!