bottle the amount she should be having is explained here here but if you still can't get your head around it just say [hsmile].
Think that 5 to 6 hours in the day though is too long, especially for a baby so young. Know that I would struggle going that long and like you say, you really need that stretch at night, not during the day.
Have a read of this on reverse cycling. It is aimed at bfing mums but lots of the tips will be relevant to you too [hsmile].
Some things that might help are getting her up and fed and changed into daytime clothes pretty early, say 7 or 8, whichever you are happiest with.
Then make sure she gets some daylight, even if its just wrapping you both up warm and going into the garden and having a cuppa. The sunlight will help her realise it is daytime and the chemicals the brain produces in sunlight will help her sleep more at night.
Try and do some things in the day too. I know she won't be awake much at 10 weeks but she may enjoying a swimming or baby massage class or just going along to your local playgroup. Children's Centres usually have a good range of activities to try.
Make sure she has a relaxing bedtime too, with a lovely warm bath and some comfy night clothes.
There are some good tips here as well. [hsmile]