So, broadly speaking, the "Vedic Period" refers to the late stages of the Indo-Aryan migration into the Indian subcontinent and the concurrent development of early Vedic literature. But let's expand upon that a little. Between 1500 BCE and 600 BCE we see a movement of the Indo-Aryan ethno-linguistic group from present day Iran into India and Bactria (Afghanistan, India, Nepal, and Pakistan). You mentioned them being "white-skinned Persians" which is broadly accurate but too loaded with cultural baggage for my liking I would discard both parts since the Persians divirged from the predeccessor culture of the Indo-Aryans about the same time the Indo-Aryans migrated to the Indian sub-continent and the comment about white skin is not really possible to verify and they probably didn't resemble any modern day ethnic group exactly. It is better to think of them as part of a much larger, but divergent, group of cultures.

In any case, as they moved south they encountered, in some capacity, the existing population. The exact ethno-linguistic makeup of the pre-Indo-Aryan inhabitents of India is a major disagreement among scholars and something I don't feel completely comfortable adressing since it is tied up with issues of racism and pan-Dravidian Nationalism as well as outside of my area of expertise. In any case, I think thinking of them as simply Dravidians may over simplify the issue. This encounter may have been as early as the initial migration period which led to displacement of the Pre-Aryan population, but others have suggested that the Indo-Aryans moved into a gap after their predecessors migrated south. This mixing was probably quite gradual but the essentials of the Vedic religion probably came predominently from the Indo-Aryans.

The Vedic religion seems to have come from, at least initially, Indo-Iranian and Indo-European religion, sharing deities, legends, and rituals. In the earlier parts of the first millenium BCE it began to take on greater traits of monism and henotheism not present in its earlier form as evidenced by the later additions to the Ṛɡveda and the Upaniṣadic literature from this period. 600 BCE marks neither the end of Vedic literature nor the begining of Hinduism, but rather the beginnings of the Mahājanapada period politically and the Śramaṇa period philosophically. However, by this point there was a sort of recoɡnizable reliɡious tradition often called Vedic Religion or Brahminical Orthodoxy focused around the Vedic deities.

The Vedic religion, while the root of Hinduism, is not identical to Hinduism as we know it, which largely began during the last century BCE and tge early centuries CE with the further development of the "Āstika" schools of Indian thought and the compisition of the Purāṇas. The Vedic religion was a sort of predecesdor focused on Vedic gods and ritual sacrifice, rather than on more modern Hindu gods and philosophy.

I went over this kind of fast because I'm on my phone, but would be happy to clear things up or add more if you have further questions or need clarification.