well, Eternal Pets have the same drop rate of Eternal Items. max Luck & Eternalized Items are the way to go.
since Pets require an Enslaver to drop them, it tends to take longer to get an Eternal Pet compared to Eternal Items.
this part of the Thread is specifically for 3.0. if you read the whole Thread, there is a lot of good advice from questions being asked and answered. hope it helps you on your Eternal Pet Quest.