Hello and welcome to BW forums
As Kate says, it is normal for your young baby to want to be near you all the time but you can gradually and gently teach her that she is safe and cared for and that it's okay to sleep in her cot. It does take a lot of time and effort, EASY isn't easy and Tracy said this in her BW books. Waiting a few weeks for LO to get older is not likely to make a huge difference to LO and isn't likely to make sleep training any quicker but it may make a difference to you - you need to be ready and if you don't feel ready to tackle this right now then it might suit you better to hold off for a while.
Because of how much time, energy and patience it takes to gently sleep train some parents choose to work on just one nap per day to begin with. Perhaps this option would suit you? Overall it takes longer to reach the end goal but it is certainly a move towards it and is less taxing on tired parents. If you choose to do this I suggest you pick the same nap each day (the first nap of the day is usually a good place to start) as LOs pick up habits per nap and get used to the daily routine which will work in your favour. You are likely to need to shush/pat through the whole nap to begin with or at least for 20 mins after LO has fallen to sleep to get her into the deep sleep phase, and then perhaps again at the transition from one sleep cycle to the next and into deep sleep again. This is described in the BW books as often parents put baby down asleep and discover they wake up after 5 or 10 mins. When working on one nap per day you could then use the sling for the other naps.
We don't recommend co-sleeping at night due to SIDS risks. It is of course your choice. I'd aim to get her into her own cot or bassinet as soon as possible, next to your bed where you can reach out and put a hand on her through the night to help her feel close and safe but without co-sleeping. This can also help LO gradually learn to sleep without your help as they are responded to with a reassuring hand and shush/pat through the night but without being in the parent's bed.
hope this helps, please do let us know if you have more questions.