Yes, it is possible to somehow lose Dogmeat and progress onward. But, you can get your canine friend back on the PC version by using some console commands. But you can recover him easily just by using a simple console command.
The code to get Dogmeat back by using the Tilde key (~) on your keyboard.
For a long time PC gamers, they should know that this command key was used for codes like God Mode, Delta Q Delta and other helpful console commands. Well, in Fallout 4, users can find Dogmeat by its ID number of 0001d162, according to the source.
First open the console command by hitting Tilde (~) and type “prid 0001d162.” after that type “moveto player,” and close the command console by hitting Tilde (~). This will bring Dogmeat right next to you. Remember, this method of getting Dogmeat back after you send it somewhere will only work on PC, due to the Tilde or ~ key.
Now you can travel across the wasteland or the Commonwealth with your four-legged friend again, and if this happens later down the road, Tilde is the answer.