Hey BluePanda, good photos depend on the photographer, not the camera. It's nice to have a DSLR, and as you get better and more advanced you'll probably want to invest in one. It gives you more versatility, importantly.
But you can do so much with your average point-and-shoot now. Because point-and-shoots AREN'T average anymore. They can do what professional cameras could only twenty or thirty years ago. Think about creating pictures with strong composure. That's the key. Think: what am I taking a picture of and what am I trying to say? How can I create a photo that emphasises that? Look at the work of famous photographers, as well as reading up on tips.
One technical area you'll probably want to get your head around first, is lighting. Photography is the art of light, after all. Invest £20 in a reflector (or make one for a few pounds) and you'll be able to take photos with great lighting.
Good luck and welcome! I'm new myself!