You will probably run out of payload before tow capacity.
Realistically your tongue weight will come in around 13% of loaded trailer weight to tow properly.
Once you have battery. water, dishes and all the other junk we all carry 500-1000 is quite normal. Let's say in the middle for you that is around 7000lbs x13%=910lbs. Now add 100 for your WD hitch, 300 for you, the 60 for the dog and you are at 1360 lbs. This leaves you about 160 lbs left for anything else to carry in the back of the truck or things not covered.
Close yes but you will probably be close to the max. Common issue is that most just read the towing capacity and not the payload in a half ton. That is where the challenge comes in. I have been there and switched to 3/4 ton and that takes care of the payload issues in that weight category as I am similar to you.