DD(5) still doesn't sleep through. Was breastfed and woke every two hours for the first few months.
DS (18months) has slept through since 3 months. For the first few months sleeping through would be from about 10pm until 7am, he would cluster feed from 6pm until 10pm. Also breastfed.
Friend's DS (10 months) has never slept through, wakes a couple of times in the night and is up for the day at 4.30. Formula fed.
It is complete luck of the draw, depending entirely on the child, unless there are extenuating circumstances such as milk supply.
Providing there are no current issues with breastfeeding then a single bottle last thing at night shouldn't affect your supply, except for the obvious dropped breast feed. And providing you express off just enough to feel comfortable if your breasts begin to feel full mastitis shouldn't be an issue either.
However, 6 weeks is still very little, and in my experience the first 3 months are the hardest. After this, unless ill, teething or otherwise distressed, feeds are generally fewer and further between.
The other thing to bear in mind is that even if you give a bottle, your baby may not sleep any longer, and you could end up in the position of having to work a bit to re-establish the dropped breast feed if you decide to go back to it.
If you have a partner who would be able to give the bottle so that you can grab the extra sleep for the duration of the feed then it's an option, or as per PP, a dummy might help if it's the sucking reflex your baby needs.
But if you're looking for a miracle solution, there really isn't one. In my case it was just waiting out those first three months - with both.