If you are going to switch from the Sony to an interchangeable lens SLR, main difference will be that you wont have the same zoom range to begin with.
I have the 3200. Yes, I can crop a LOT to magnify subject in post-process and still keep pixels in the picture.... To be honest, I've been doing that for years, from a 7.1Mp 3x 25-105 equivilent zoom compact, which has been my main digital camera; and sizing down to 800 on the wide-side for screen/web display anyway, crops have tended to have more pixels than re-size display image.... may be food for thunk in that.... your Sony probably has a lot of redundant quality to begin with.
But, swapping to the D3200...kit lens is 18-55, that's 27-82.5 'equivilent, and at f3.5-4.5 not only shorter in zoom range than your Sony, but also slower... BUT should be 'better' glass.
You would likely find that little extra 'wide angle' a loss, and you'd be finding that little extra zoom 'reach' more of a lack, more often... 80-120 is quite a big jump.
Cropping from bigger pixel image, you'd get it back, and that bigger pixel image would probably be a 'better' image from the better glass, but you'd be cropping a lot more tightly to get the same composition.
But of course, with the SLR you could get another lens to suit your needs..... which is where it starts getting expensive!
the kit 18-55's are not worth much 2nd hand; and bundled with the body, kits are often cheaper than body-only price; so you have to treat it as a freeby to get you started; another lens, either a 55-200 or 55-300 to extend zoom range, or something like a Sigma 18-200 'Super-Zoom' would probably double the cost of the camera! BUT, again, good glass, and zoom range that would give 27-300 'equivilent', you have the extra zoom 'reach' in the glass, you wouldn't have to do it digitally in Post-Process!
Either-Way though, its a LOT of money for little gain in what you want to do.
Outside the box? Unless you have need or or would like to explore SLR photography more; then some of the other bridge or super-compacts have pretty astounding zoom ranges these days. O/H has a Nikon L310 I think; not a camera I can thoroughly reccomend its a real point & press special; but as such, it packs 16Mp resolution, and I think its a 21x zoom range thats equivilent to about 18-250 on a crop sensor camera, or 27-180 in 35mm, and there's a bigger brother that offers 30 times zoom.
The Party trick in your Sony, though is APS-Crop sized sensor, same as in an entry level DSLR, and that's worth a fair bit as far as IQ goes.... but as said... there's probably a fair bit of redundant IQ you never exploit anyway, even at a 'lowly' 10Mpix, unless you are making prints and big ones from image files.... on screen, 1024 ish on the wide-side display resolution? EVERYTHING is going to be resized down to about the resolution of a 1.3Mpix camera anyway!