Thank you all very much for the responses. This is a really important issue to me. I'm new to photography, I really enjoy it, and I don't want to lose my enthusiasm.
I've posted this query on a couple of forums, and the replies have helped me clarify the issues. Here's how I see it now:
Since I am literally starting from scratch, I have to develop two skills. One is learning the camera and what it can do, and the second is learning composition.
To me, composition skills are paramount. That's where the creativity is, to see the shot. I need to learn how to recognize a good photograph, how to frame it, and so on. As all the pros keep on saying, the photographer is far more important than the camera.
After that, comes how I technically achieve it using the camera at hand.
I have a great camera that is easy to use and which most of the time will let me concentrate on composition. So, why am I considering a DSLR? Sometimes, especially in low-light situations indoors, or with macros outdoors, I just can't get the shot on the Sony. So, I have three options:
1 Live with it and move on to the next shot. Not really an option - I can get along without the macros, but not without the family pictures.
2 Learn how to get around the limitation on the Sony, and probably purchase an external flash.
3 Use a DSLR which will enable me to get more shots than I can at present. Of course, I'll still have to learn how to handle even lower-light at some stage.
So now, my question to you is more focussed. Which will allow me to be more creative - to keep shooting on the Sony and channel some energy to tackling low-light issues, or to learn a second camera so that it can take care of the majority of low-light issues for me?