Yup, it's really really normal for babies to only sleep on you when they are still tiny (and anecdotally I think this is especially true for any baby born small or early, even slightly early).
It will improve quite soon honestly, and you're not creating bad habits by having her sleep on you. Try her in the basket every few days, you will find she gradually gets better at staying asleep there. The sheepskin tip is good. Similarly I used to wrap DD in a thin blanket when feeding her to sleep, then transfer her wrapped in the blanket, it helped. Propping her on her side also helped. You can also buy things like the Sleepyhead or the Cocoonababy which aim to make a newborn feel happier on their back, but these are pretty expensive for quite a short time of use.
In the meantime, it's about you getting enough sleep somehow. Will she sleep in her basket in the day? If so then try to sleep then as much as you can. At night, I learned to sleep sitting semi upright with Dd lying tummy down on my chest and my arms around her (with multiple pillows to support my back, head and elbows). I was in the middle of a large double bed and it felt safe. Also SIDS advice says this is fine.
There is a growth spurt at about 3 weeks, so don't despair if it feels like she's always feeding and you haven't got enough milk - she is feeding a lot to increase your supply so hopefully this should get easier soon. You could try introducing a bottle at about 4 weeks if you want, do you have a pump to express breastmilk? (best time to express is usually straight after the morning feed) that could enable DP to give a feed and give you a break.
Once she's a few weeks older you could try keeping her awake a little bit more in the day to try to rebalance her day/night perception. However I wouldn't do it now because she still needs so much sleep at this age, you could end up with an overtired baby which is awful (trust me!). Also you may find she sorts out day/night herself in the next week or two.
Good luck - you're doing well.