No, and I found that out the hard way. If your pet has a talent, you cannot socket a jewel with the same talent. You can socket a different damage jewel (death bringer, pain giver, pain bringer), but make sure the jewel and the pet talent are not the same.
Once a talent has trained, we can't equip a jewel for the exact same talent. So if your pet knows Death Dealer, you can't give it a Death Dealer jewel. The option will be greyed out.
Alia Misthaven