The present genetic studies attribute agriculture in South India to Haplogroup J2 and Haplogroup L1 people. I take the definition of agriculture as rice farming with respect to South India. However, many parts of Karnataka and North-West of Andhra Pradesh are not really rice eating regions. But first, let's try to fix J2 and L1 clan members.
I am not really sure about Y-Hg-J2b2 people. Their frequency does not give much clue. I would put them with original South Indian tribal population(that is till we sample fishermen).Before the emergence of agrarian South India, the tribal society saw new members from North-West of India in the form of shepherds and cowherds. Before their entry the original inhabitants of South India were Haplogroup R2, H(not H1) R1a1 and J2b2 clans. These shepherds and cowherds mainly belonged to Y-Hg-L1. Many of these people also diversified into toddy tapping in the later period.
The lactose tolerance reaches only 30% in South India*. So milk made entry relatively recent or milkmen came after tribals and fishermen to this land. However, I have also read that Indians have very high incidence of alcohol intolerance. It looks like binge drinking is not really our mug of alcohol. I believe the research must have been conducted on North Indians. South Indians, I would say, certainly are not that delicate(with Telugus and Malayalees leading the way). Anyway, Soma drinking Indo-Aryan genes must be really a thing of the past. That shows toddy tapping could be one of the oldest professions along with fishing in South India. Most likely, tribal South Indians lived close to water bodies in the regions abundant with Palm trees and ate fish and tapioca and drank Kallu.
After cowherds and shepherds migrated to South India, the eating habits changed(The origin and spread of Indian water Buffalo is not clear; I would speculate they were domesticated for milk and farming in North and North-East India then along with cowherds and farmers these also migrated to South India) .It should be Indo-Aryans(also Vaidiks of old era) who were the beef eaters but with migration of these people beef made its entry into South Indian plate. The present beef eating Malayalees(probably, the only Hindu community at present to keep eating beef) were in fact the last ones to eat beef. Hence, along with fish, tapioca(cassava root) and kallu, Malayalees ate beef (and are still nostalgic about it. Sometimes, they take it as staple diet instead of rice centred food).
And Parashurama gave the land to Brahmins
I discount J2 and L1 as mainly responsible for agriculture in South India because rice farming obviously look like being spread from North-East of India and L1 absolutely do not have any presence in North-East of South India too.
Interestingly, English word "rice" is supposed to have Indo-Iranian origin. The root is represented in South Dravidian-1(*ari) and South Dravidian-II(ari-se in Telugu)(Find the reference at Starling database). So it looks like the word is a borrow from Indo-Aryan. However, none of the Indo-Aryan languages show the derivative of that word for rice. A strange situation. Probably, something to do with the late adoptation of rice farming in North-West of India. However, if rice farming was not part of Indo-Aryan speaking population in those parts then how come the word for rice is part of North-East Indo-Aryan speakers who moved South India and also Europeans. I do not know. I think to escape from incoherency people just don't connect many things together. Anyway, our population Geneticists lead the way.
As I said before, rice farming started in North East India and moved to Gangetic planes. The Brahmins who migrated to South India from those areas also brought the knowledge of farming with them. In fact, in South India only Brahmins, except for coastal Andhra (as the region is close to North East of India hence tribals could have diversified into farming on their own) most of the other parts of South India had only Brahmin land lords. In small regions like coastal Karnataka(Tulu Nadu) and Kerala almost all the agriculture lands were once belonged to Brahmins. Many tribals started working in these lands as supervisors or as labourers. Many supervisors then independently became landlords or acquired the land from Brahmins in regions like Kerala. The emergence of tribal farmers also paved the way for rapid expansion of Haplogroup H1 in South and Central India. Most likely Haplogroup H1 is originated in North-East of India(Bengal, Orissa areas).