Was Shireen Baratheon's doll intentionally infected with greyscale?

Short answer: No. There is no evidence. As someone also added, this is not how it happens in the books in the first place.

Let's stick to show and elaborate a little this Dornish trader story. Also as other noticed, Oberyn is not a kind of man that would kill let alone infect innocent child for some distant revenge. He hates Tywin and Mountain, and instead of killing already defeated Mountain he still wants confession because he wants to be sure whom to blame. To focus his anger on leader of rebellion who surely didn't give such command, then do something against not even his brother but his newborn niece is just mental. He waited for years and still wants confession whom to blame, no way he would do that.

Would any other Dornishman want this? Seems unlikely. We don't know that Stannis had any personal enemies who would want something like that happen to him. Would someone be disgusied like Dornishman or was it faceless man? Still, no reason to do it to Stannis.

Politically, also no point. Stannis rules Dragonstone and some surrounding islands and fisher villages. It is not juicy at all. If he remains without heir, lands go to his brothers or nephews. Nobody else can't jump in. Not even pointy beard Littlefinger seems likely to have any interest in Dragonstone. Plus at the time of her birth it is not certain that she would be his only child, so makes no sense really.

I gave it some tohugh and here is the only wild theory why would someone actually want that: if someone actually wants her exactly and knows how to cure grayscale. This would be the only way to get newborn baby of lord of Dragonstone. Kidnapping her is pretty much impossible, plus it makes much of fuss. If someone needed Shireen because she has king's blood or whatever and wants to do it secretly and knows how to treat grayscale, this would be a way to get her eventually dropped to Valyria and she would be forgotten. Nobody would know if somebody waited there, snatched her and healed her. We could hypotesize about various people who would treasure such possesion as Baratheon princess with Targaryen blood and most likely they wouldn't be from Westeros :)

If this still sounds unlikely and makes no sense, well same here. Like I said, this is just a wild theory I could came up with. Most probably it wasn't intentional.