Would the +1/+1 counter from Curse of Stalked Prey save my creature?
No, the blocker would be destroyed.  From the comprehensive rules dealing with the Combat Damage Step

510.2. Second, all combat damage that’s been assigned is dealt simultaneously. This turn-based action doesn’t use the stack. No player has the chance to cast spells or activate abilities between the time combat damage is assigned and the time it’s dealt. This is a change from previous rules.
510.3. Third, any abilities that triggered on damage being assigned or dealt go on the stack. (See rule 603, “Handling Triggered Abilities.”)
510.4. Fourth, the active player gets priority. Players may cast spells and activate abilities

The state based action that destroys is 704.5g.  So although the ability triggers it is placed on the stack.  State based actions are dealt with before the stack is, and thus, the blocker dies.