You might not be able to target Doug with your spells and abilities, but you can remove his blockers and go for his throat. The only problem with that plan is Doug’s high life total; 20 life is nothing to sneeze at. You do have a creature that can gain +1/+1 counters, so it’s not impossible. You just need to find a way to get those counters, and it’s going to be painful.

1. Tap three mountains to add (two used as generic mana), four plains to add  (two used as generic mana) and Slayers’ Stronghold to add to your mana pool.
2. Spend and tap Akroan Mastiff to activate its ability. Choose to tap Doug’s Spirit of the Hearth.
3. Exile Pillar of Flame from your hand to cast Cave-In.
4. In response to Cave-In, spend to cast Harm’s Way. Choose to prevent 2 damage that Cave-In would deal to your Blood Hound; instead, have Cave-In deal this 2 damage to your Lava Hounds.
5. Resolve Cave-In. Cave-In deals 2 damage to each creature and each player except for your Blood Hound; Cave-In deals 2 additional damage to your Lava Hounds. Doug’s Jungle Lion, Leonin Relic-Warder and Cat Warriors die, as well as your Akroan Mastiff and your Lava Hounds. You are now at 5 life. Doug is now at 18 life.
6. Blood Hound’s ability triggers, and you put two +1/+1 counters on it. Blood Hound is now a 3/3 creature.
7. Leonin Relic-Warder’s ability triggers. Return your Words of Worship to the battlefield under your control.
8. Angelic Renewal’s ability triggers. Choose to return your Lava Hounds from your graveyard to the battlefield under your control.
9. When Lava Hounds enters the battlefield, it deals 4 damage to you. You are now at 1 life.
10. Blood Hound’s ability triggers, and you put four +1/+1 counters on it. Blood Hound is now a 7/7 creature.
11. Spend to activate Words of Worship’s ability.
12. Spend to cast Needle Drop on Doug’s Qasali Ambusher, since the Ambusher has been dealt damage this turn. Qasali Ambusher dies. Your card draw from Needle Drop is replaced with Words of Worship’s ability, and you gain 5 life instead. You are now at 6 life.
13. Spend and tap Erratic Portal to activate its ability, targeting your Lava Hounds. Allow the Lava Hounds to return to your hand.
14. Spend to activate Belbe’s Portal. Choose to put Lava Hounds from your hand onto the battlefield.
15. When Lava Hounds enters the battlefield, it deals 4 damage to you. You are now at 2 life.
16. Blood Hound’s ability triggers, and you put four +1/+1 counters on it. Blood Hound is now an 11/11 creature.
17. Declare the start of your combat phase, assigning your Blood Hound, Lava Hounds, and Thraben Purebloods to attack. (You may assign Lava Hounds to attack this turn because it has Haste.)
18. Because Doug has no untapped creatures, he is unable to block your attackers. Your attacking creatures deal a total of 18 damage to Doug, defeating him.