I'm sitting at:

Tier 1 Level: 20 Health: 10 / 46 Strength: 52 Defense: 46 Speed: 45 Intelligence: 40 AP: 2

I've always had a habit of wanting to over train for tasks and I want to make sure my battle pet is considered decent before trying out those Battle Quests.

You won't be able to beat many opponents in battle quests yet, but it's still totally worth it to give them a shot! EXP costs scale up with tier, so even though, for example, you'll beat fewer opponents with a tier 1 pet, it will also cost you less to buy stats with the experience you do get from battle quests than it will at tier 2!

There is no penalty for battling here before your pet is ready. If you lose a battle, you can heal your pet back to full at the healer. They don't die permanently. In addition to battle quests, there are easy default and secret opponents you can attempt to battle for exp and sP. Outside of battle quests, the opponents will get harder the more times you beat them so be mindful of that.

It has been years, but I remember when WIl-O_Wisp was the weakest opponent and I think I kept losing to it. I think you can comfortably beat, like, 2 enemies with that stat.