Hathor is a sky goddess, known as "Lady of Stars" and "Sovereign of Stars." Her birthday was celebrated on the day that the dog star, Sirius first rose in the night sky (heralding the coming innundation). She was originally a personification of the Milky Way, which was considered to be the milk that flowed from the udders of a heavenly cow. As time passed she absorbed the attributes of many other goddesses but also became more closely associated with Isis, who to some degree usurped her position as the most popular and powerful goddess. Yet she remained popular throughout Egyptian history.
More festivals were dedicated to Hathor and more children were named after her than any other god or goddess of Ancient Egypt. Her worship was not confined to Egypt and Nubia. She was worshipped throughout Semitic West Asia, Ethiopian, Somlia and Libya.
Sirius rises at different times depending on the year and location, usually around the first of August. I was unable to find a definitive list of dates for you, however I did find two websites, which when used together will show you how to determine the birthday of Hathor, and the exact day and time of the rising of Sirius in your area. They are:
Compiled from various sources.