6 weeks does seem a bit too early. If your baby is taking 8-9oz every 2 hours or less and waking frequently for feeds during the night, then hungry baby milk could help her avoid being sick and over-eating.
My DD2 would feed every 2.5 hours during the day at that age, and only went to a 3 hourly routine at 12 weeks, and never wnet 4 hourly during the day until after she was on 3 meals a day (about 8 months).
Hungry baby milk doesnt contain any extra calories, nutrients or goodness than first milk. It is just harder to digest, meaning it satays in the baby's stomach for longer making them feel full. It can cause constipation and discomfort, especially in younger babies. Its really ment as a helpful tool to delay early weaning, so babies can reach 6 months on a milk diet until their stomachs are ready for food. xxx