Tips on helping Dogmeat survive until the end in Fallout 1
Solution 1:
With the information coming from the wiki itself, there are no rewards for keeping him alive. However, you can keep him alive through all those mutants (in what I assume is the following segment, I have not played the game myself):
In the Vault Dweller's memoirs, it is disclosed that Dogmeat died in the Mariposa Military Base after running into a force field (although in the game, it is possible to survive the military base with Dogmeat alive - usually by sealing him inside different rooms to protect him from the super mutants).