It's possible to have a planet with those parameters; it just won't be completely like Earth.
First, the values for surface gravity and mean density are consistent with the mass and radius you've chosen, so quantitatively, you're fine. Where things get interesting is the composition of the planet itself.
Terrestrial planets start their lives with envelopes of hydrogen and helium -- like giant planets. However, their gravity isn't that strong, and various atmospheric processes involving energy from the parent star means most -- including Earth, Mars, and the other terrestrial planets in the Solar System -- lose these envelopes. The dividing line ends up being somewhere around $2M_{\oplus}$ (see e.g. Lammer et al. 2014).
Above $2M_{\oplus}$, you get planets in the murky range between super-Earths and mini-Neptunes. Both have thicker atmospheres than Earth, with mini-Neptunes resembling low-mass gas giants. The boundary between these two groups is somewhere around $\sim1.75R_{\oplus}$ and $\sim2R_{\oplus}$ (Lopez & Fortney 2013) -- larger than your planet. So you're looking at some sort of super-Earth, a terrestrial planet with a thicker atmosphere than you might have expected. (This probably makes sense -- after all, the surface gravity is higher than Earth's making it easier to retain hydrogen and helium!)
As for composition -- numerical models of planets of your mass and radius indicate it's like 5% an iron core with the remainder a mix of water ice and silicates (Seager et al. 2007 -- check out Figure 4!). It's unlikely to be more than 50% silicates; planets about that often have larger iron cores. So perhaps 5%/50%/45% is a reasonable iron/silicates/water ratio, something comparable to Ganymede. My guess is that the calculator was giving you weird core density because you can't attain that mass/radius/density/surface gravity with just a combination of iron and silicates; you need water to lower the mean density.
In short, you've got a partially watery or icy world with an atmosphere thicker than Earth's. It's definitely plausible!