The D3100 is Nikon's entry level camera - it's probably equivalent to the 1100D on Canon's side; and since you're using the kit lens 18-55 f/3.5-5.6 VR, you have a disadvantage in terms of lighting compared to those using brighter lenses (my guess is that ur probably shooting at the 55mm end, which restricts light even further).
If you want sharper pictures or to achieve the bokeh (blurring out everything except the main subject), you'd need better lenses. Like what other suggests, 50 f/1.8 or 1.4 is always a good place to start given the cost-performance - though it's going to be less convenient than zooms. Of course, if you got cash to spend, you can go all the way to the 70-200 f/2.8 VRII or other recommended portrait primes.
As for the question of whether it's the right camera... well, the D3100 can do the job, but if you have the cash, you can always find better options.
If you really want to find gears to add w/o spending too much, go with the 50 f/1.8 and a powerful flash like a used-SB900 (if you have more cash, feel free to go for better gears).