Canis Major's first article already ties Sirius to the Egyptian Nile flood. What it has no room for is that Sopdet, the Egyptian name for the star, was not simply an omen but a figure in her own right, paired deliberately with the neighbouring constellation of Orion.
Egyptian star ceilings personify Sopdet as a woman, sometimes as a cow bearing a star between her horns, walking behind or beside Sah, the striding figure at Orion identified with Osiris. The pairing is not incidental: Sah and Sopdet are the two most securely identified figures in the Egyptian decan system, thirty-six star groups used to mark the hours of the night, and their relationship, consort or companion depending on the source, was read as mirroring the relationship between Osiris and Isis, with whom Sopdet came to be identified.
The heliacal rising, the star's first reappearance in the dawn sky after weeks of invisibility, was the calendar event, and it fell close enough to the actual onset of the Nile's annual flood that Egyptian record-keepers used it as the marker for their new year, a practical function bound to a personified figure rather than to an abstract star.
None of this involves the dog at all. The Greek hound following at Orion's heel and the Egyptian goddess accompanying Sah are two completely different relationships built on the same two points of light.