Congratulations on your lovely baby.
This sleep issue is something many of us are unprepared for as in our culture, we have an image of babies sleeping in cots and think that's normal. The reality is that for many (most?) babies their instincts are crying out to them that they want to be next to you. This is perfectly normal, but unexpected as it's one of the many things that's not discussed about motherhood before you get there (no idea why this is!).
Your baby has been inside you for all if her life ubtil very recently, it's not surprising she still wants to ge close tp you. Also posdibly worth reflecting that human babies are born earlier than most other mammals. If you think about it, many mammals are born able to stand and move independently from day 1. But because we have large heads because of our big brains, and small birth canals because we walk upright, our babies are born pretty early. Because of this, they are much more vulnerable and helpless than most other mammals when born, and need to be close to us. Sometimes the first three months are called the "fourth trimester".
Another thing not often discussed is that babies want to be close to you for more than just milk. Again we at down how important this is, in our culture, saying things like "she's only feeding for comfort" as if comfort wasn't important! Actually I imagine comfort and knowing their mother is close by is probably very important to a baby.
Also there are important biological reasons a baby wants to be close to its mother. Babies are supposed to sleep in the same room as you till 6 months for example, not just so you can keep an eye on them, but also because being in proximity to you actually helps them learn to regulate their breathing when asleep.
Also, sleeping next to each other helps establish breast feeding, and very often leads to much improved sleep for both mother and baby (not always! But certainly for lots of people).
I expect you jnow that breastfeeding supports your child's immune system, but did you know touch is important here too? Feeding expressed milk from a bottle wouldn't be quite the same: IIRC when you feed your baby, your body takes on your baby's disease-causing microbes, through their saliva on your nipple, then your body makes antibodies and gives them back to the baby in your milk, that's amazing! Your boobs are like your baby's own personal chemist!
That's not to say your body wouldn't be able to do that without co-sleeping, but just to demonstrate the importance of touch and that breastfeeding is about way mire than food!
OK, essay over!
In short, it could be worth considering cosleeping, it made all the difference with mine. Look up safet cisleeping guidelines so you know how to do it safeky. Alternatively, if you're not keen on bedsharing, there are some great three-sided cots available. We had one for DC2, it was great. You can get them from German Amazon for about £100. Single best thing I've bought for my babies! My DD sleeps through in it, or in my bed. She wakes about every hour without it. I'll post a link when I'm not on my phone.
Or, if you're determined to get her so sleep in the Moses basket, go for it. But be aware that you're trying to get her to do something against her instincts. We do it for cultural reasons, we think its normal (I certainly did when I was a new mum), but all your baby knows is she wants to be near you. That's not to say don't do it, plenty of people manage to get their babies to sleep alone. Plenty however spend many sleepless nights tearing their hair oug wondering why their baby won't sleep alone like they "should" and I think it's not helpful that we don't discuss, usually, that the idea that babies should sleep alone is cultural, and not always easy, or even possible without broken sleep for everyone,