Ok, lol.
It's either a power that brings doffy closer to his objectives:
Money
Kid soldiers
Weapons
Smiles (unlikely as he took her out of the factory, and stop production, before any crisis, the factory being very safe back then)
The "other piece" (I'd like that this name catched on, Marijoa's treasure)
Devil Fruits (but not extracting them, or else he'd killed law a while ago)
Inmortality
Extermination of the Nobles
Fun?
Or that heavily threatens his objectives or life itself
the "tangle tangle fruit"? Truth Truth fruit (can't lie on it's presence? Riku want's a trial after all of this?)
A healing fruit is very unlikely, as there would be hints, by allowing buffalo to get back to the fray, or allow franky to defeat Machvise before, just for him to come back.
Right now the truth fruit seems likely, specialy with the personality of the tontattas, but it's reduntant with Violet's mind reading, and would have catched Violet that way.
–- Update From New Post Merge ---
Now that I think about it, why didn't Monet notify Doffy about Law's and Caesar's deals? Or if he knew, why didn't Doffy go to get Law the instant that he knew that he was on the island, other than keeping tabs on him, there wasn't much of a reason for him to allow Law to be there, he allowed monet to become an harpy, and Caesar's minions to walk again, but how did any of that be better than getting the key of inmortality in his hands?
Law's arrival at Punk Hazzard should be after the duel for the fleet admiral position, but it is also after his naming of Shichibukai? did he stay there once he got the title and did all the shambling? Did he wait for Luffy there? How long has he been apart of his crew?