My daughter is 5 months old now. When she was first born, we literally never put her down for the first couple of weeks. After that, we tried to put her down occasionally. (We coslept, and we wanted her sleep on the bed between us, for example. She didn't like to be put down and would not sleep if not on us for the first month.) We tried getting her to nap in various devices to no avail. So we just went with it. She was always in the Moby wrap or on a lap (mostly mine, because she nursed constantly!) for the first couple of months. When we did put her down to get her to nap, she would take a short nap (20 minutes) as opposed to a longer one.
When she was around 2 months, she expressed an interest in being put down, so I sat with her on the floor and did tummy time with her more and more. (We did it sporadically before then. People told me that if you never put them down, they'll never want to be down, but that wasn't true in our case.) I would put her down to go to the bathroom or, if I was lucky, heat some food. But she was mostly an in arms baby. (It was SO HARD!)
Around 3.5 months, she seemed okay with not being next to someone 100% of the time. I could leave her to play with her hands or a toy for maybe 10-15 minutes a couple of times a day. And she enjoyed sitting in a bouncer/infant seat sometimes, for example while we ate dinner.
Now at 5 months, she plays a little more with toys. But she still spends almost all of her time in the sling or on my lap or within a few feet of me or my husband (on the floor or in the bouncer) or in the sling or on a lap. She doesn't like to be left alone much.
She's an exceptionally happy, secure baby. Although I'm sure much of the reason for that is her inborn temperament, these months of closeness have definitely gotten us in tune with one another and created a bond that I cherish.
Follow your instincts, and don't rush her out of your arms if keeping her close feels right. Try to get other people to take care of necessary chores--you are creating a bond that sustain her and you for the rest of your lives!