I use a Rebel T1i and have taken some pretty good pictures. I have seen some INCREDIBLE shots taken with these Rebel Cameras.
Would a professional charging $400/hr use a Rebel? Probably not. Is it a darn good camera capable of taking excellent shots? You bet. Especially with better lenses in the future.
Here's two of my favorite shots I took with my T1i and the KIT LENS, and being quite mediocre myself;
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And, there are plenty of things wrong with both of these images! I didn't post those to show you what perfect shots look like, I just took those to show you what a guy who shot images that look like what you posted, progressed to a couple months beyond that. And it got better after that, and hopefully, it'll continue to get better. It just takes time. None of these incredible shots on this forum (photo of the month winners, etc.) were done with inexperienced folks. There is a lot of talent, but also a lot of know how and experienced involved here.
Point is, I haven't nearly outgrown my T1i. The Camera is still more capable than I am, I haven't 'maxed it out'. Once you have, THEN you can worry about a better Camera body, but a great camera doesn't take great pictures. Take a 1DX and start firing away with the pop up flash and poor settings, and you'll take poorer pictures than an experienced photographer would with a 5 year old Rebel. For a beginner, there are much more important things than the Camera body.
I also have some images that I WISH I could take credit for, taken with the exact same camera, by a relative of mine who is a professional photog. He shoots a 5D Mk II. He stuck one of his L lenses, a 580 EX II flash unit, and a monopod on it and shot some INCREDIBLE shots of my aunts garden. In capable hands with good glass, the Rebel series is capable of great things.
Truth is? And I can say this to ya because I'm in the same shoes as you. Those images would have looked the same with a 5D Mk III or even Canons flagship 1DX. (And your 18-55 kit lens). They just weren't setup right. That's okay! You'll learn over time.
Also, don't be afraid of full auto mode or the program modes if you aren't quite sure. They do a decent job, and the rebel DSLRs are also excellent point and shoot cameras. A lot of times at family events, where I'm just shooting memories not portfolio pieces, I just stick it on full auto. I get great memorable shots to post on facebook for everyone to remenise over. And, when possible, I stick it on full manual mode and spend time learning to shoot better by trying to re-create and then improve on some of those same auto shots using manual mode. It's a great way to learn!