Hearthpwn

I know,I know, the days before the expansion people build decks that are 70% new cards. Sigh.

 How do you plan on completing the quest?

There are 8 cards that generate cards outside your deck, excluding Primordial Glyph into glyph shenanigans. If I'm not mistaken, Antonidas' generated fireballs count toward the quest. 

How do you win the game without giants? You can't play Time Warp and Antonidas on the same turn.

The quest is about getting you in a winning condition, but not necessarily winning (more check than checkmate). You will have been more competitive on board than the spell heavy version with your elementals, and you should be able to use the extra turns attacks and mana efficiently. 

You're missing a six drop elemental. You won't be able to curve into Blazecaller.

Pyros' second form is a six-drop. You can also use your generated Flame Elementals from Igneous Elemental along with whatever else you want to play on six. 

 You're only running one secret. That's not really a secret.

True, it's two things. First, it makes the opponent wait until he has a low value spell. If you don't play it on curve, you're more likely to affect their line of play. The second reasons is that it gives you a zero-cost spell. Easy fodder for Antonidas.