It should be fine. Actually just about any of the Nikon DX digitals will work about the same for portraits with the same lenses. The D5xxx series has some AF advantages over the D3xxx series, and a few other options, including the tilt screen that can be very nice for macro work.
Perhaps you should be looking at lenses too. This can be complicated, as some are faster than others (this refers to the amount of light that can pass through it). Portrait photography used to be with an 80mm lens on the old 35mm film camera lenses. A 50mm on the newer DX models should be fast enough and at a reasonable price for the 50mm f/1.8. It's a good starting point. Note the 18-55mm kit lens is 5.6 at 55mm. This is slower and lets a lot less light into the camera, which means camera shake etc. The Coolpix is designed as a more point and shoot, with good results most of the time. Taking the leap to DSLR is rewarding and will give you better results using the balanced lens combination, then you can play with flashguns. Lots to look forward to. There are some real bargains around like the D5200 and D3200, both fantastic, but the extra for the D5200 is worth it.
If you have enough room to stand back, something in the 85mm range can still be very good on DX, and will give a very nice look, but it's better outdoors, or for head shots indoors. Too tele for full body indoors usually. 50mm is likely more useful, and the 50mm f/1.8 a bargain for its quality.
You can get a decent portrait with the kit lens, though out of focus blur will be difficult. Keep it at as long a focal length and wide open an aperture as you can. Try to make sure that your subject is as far from background objects as possible, and experiment with shooting from a lower angle.
I did a quick and dirty comparison of focus blur this afternoon. The tree line shown in this picture is very far back, and as you can see, even at wide angle it is out of focus, but at a longer focal length, it goes quite nicely blurry. The shot at 300mm is actually fudged a little in angle - had taken it at the same angle as the 18mm, the background trees would not have shown at all, and only snow would be there. The longer your focal length, the easier it becomes to select what will or won't be in the background without significantly changing the subject.
The pictures were taken with a D3200, and the kit 18-55mm lens and the 55-300mm lens.
Nice. Good placement of background and foreground objects such that even though they are not entirely obliterated, they become abstract compositional elements rather than subjects.
Comments
It's a good starting point. Note the 18-55mm kit lens is 5.6 at 55mm. This is slower and lets a lot less light into the camera, which means camera shake etc.
The Coolpix is designed as a more point and shoot, with good results most of the time. Taking the leap to DSLR is rewarding and will give you better results using the balanced lens combination, then you can play with flashguns. Lots to look forward to. There are some real bargains around like the D5200 and D3200, both fantastic, but the extra for the D5200 is worth it.
You can get a decent portrait with the kit lens, though out of focus blur will be difficult. Keep it at as long a focal length and wide open an aperture as you can. Try to make sure that your subject is as far from background objects as possible, and experiment with shooting from a lower angle.
The pictures were taken with a D3200, and the kit 18-55mm lens and the 55-300mm lens.
http://jmp.sh/triskfF