The camera you have at the moment is fine...
Work on the basics, and getting the best you can out of it.
D90 like iwols, or a D3200 like mine, with a pair of kit lenses to give you as much zoom as your Sony, is like to be an £6-7-800 investment if you bought new; probably £500 ish
second hand.
But the big 'leap' in camera, will not deliver such a big leap in photo quality, unless you know how to use it properly and have the basic techniques to exploit it.
There are a few things about such a camera that might get you better pictures, straight out the box;
Being bigger; you wouldn't be so blase in your camera handling; you would have to hold it properly; and you would have to hold it in two hands, as the zoom is worked by holding and turning the lens barrel with the left hand while right hand grips the camera. & presses the shutter button..
Having optical veiw-finder; you are likely to use that instead of the view-screen, so hold the camera up to your eye, where again, its more likely to be better supported in traditional photographer 'pose' elbows tucked into waste making a trestle for it, rather than holding it away from your body so you can look at the screen.
And... by dint of sink-or-swim logic; intimidated by a more 'professional' and sophisticated bit of kit, that looks like you HAVE to know what you are doing with it, rather than consumer friendly compact that doesn't suggest you need know more than how to switch it on, point & press; you are likely to be more diligent, and put some time into reading the instructions.... or if you had the D3200, using its 'Tutorial' mode, stepping up to the mark and getting a bit more serious about taking pictures....
BUT... you don't NEED to buy a fancy camera to learn how to hold or use a camera!
And a little bit of getting 'clued up'; learning how the camera works; how to get the best from it; and a little work on your technique and 'discipline' in actual photo-taking, and you ought to be able to get pretty cracking shots with that little camera.
While I have the big DSLR and numerous Film SLR's... over the years, I have taken more, and probably more 'good' photo's with 35mm compact cameras or pocket digitals.
That is actually my all-time favorite camera. Yes, I know there's three of them. They are all the same; but my real ultimate fave is the one at the bottom with the flash detached... and I have had it since I was ten years old; it's been 3/4 of the way around the Northern Hemisphere, from North America to Asia with me and taken countless thousands of photos... so is consequently a little 'worn out'! Hence the other two... so it can be happily retired!
Fixed 35mm lens, and little manual control other than exposure compensation; it isn't hugely versatile; certainly less so than your Sony. BUT.. little bit of know-how to get the best out of it; and I have sets of photo's containing pics taken with that camera, mixed with others taken with my 'fancy' cameras, and you would NOT know, which camera they were taken with, unless I told you.
The fixed focal length is a little constraining, lacking zoom reach; and it's not so good for close-up photo's; but all cameras have their limits, and its a case of knowing where they are, working within them or exploiting know how to push them into the margins.
Loath, until recently, to spend the big money needed to get a Digital SLR, when I have a bunch of very good film ones, for the few instances where I really want to venture beyond what I can do with a more mainstream consumer compact; for the last ten years, I have been using digital compacts for most of my photography... and nothing as 'powerful' as you have in your pocket!
A 'cheap' fixed focal length 'lens-less' compact; has been general purpose camera, and actually rather good for close-up macro work.. (I take a lot of detail shots of bits of engines or old motorbikes or Land-Rovers to show how to change brake pads or fix clutches and stuff) While for general family pictures, I've been using a little Kodak 7Mpix camera with mere 3x Zoom, with almost no manual control, and very limited ISO range and things.
YET I have managed, with a little know-how and a little basic technique to take fantastic pictures (to me at least!) with them.
It's the old argument;
Good Cameras don't take Good Pictures - good PHOTOGRAPHERS take good pictures.
By all means check out 'better' cameras; but do bear that in mind.
Just getting a more serious SLR camera, is unlikely to get you better photo's; probably will.... but it will be as a by product of YOU getting more serious about how you use it, as much as any capability of the camera... and you could do that with what you got, believe me.
When I bought my Nikon this Christmas, being honest with myself; I knew that I REALLY didn't 'need' it, and for digital convenience; could have got myself a much cheaper bridge camera; and done as much with it. There is really only one feature of the DSLR, that I can truly say is an advantage over a bridge or compact for my photography, and that is the optical view-finder, for when tricky lighting makes the view-screen a bit hard to see.... That 'niggle' has vexed me on probably less than a hand full of occasions in the last decade!
And I take a lot of photo's; over wide ranging subjects, from general holiday snaps and family photo's; through my mechanical illustration macro-photography, to fast action motor-sport, to low-light rock gigs; I can really push a camera into those 'margins'... YET... still hard to justify a DSLR as something I NEED to be able to get those shots.
If you want to get more serious, then, and you WANT to feel you have 'serious' camera to go with it; then a DSLR might be part of the process of stepping up your game.
But... you ought to be able to step up your game and go a LONG way with that little camera you already have....
And a tip; even if you DO decide to get an SLR.... don't be tempted to trade the Sony in to get it! Keep it!
As said, it is a powerful little tool; and if you step up your game and get more serious, wit a DSLR... good chance that you will start to appreciate just how powerful that little Sony is.... and as the more portable and pocketable camera, more likely to take it with you, when you don't set out to take serious photo's, and dont want to be lugging the big one about... in your pocket, in your hand-bag... its there, and you are likely to end up taking even more pictures with it, like I did that little Olympus XA.
.