Peter Hrm, if you're doing it mainly to learn graphics programming, you can definitely do that without a dedicated GPU, and on whatever computer you're using right now. For example, in my laptop, I don't have dedicated graphics, but instead have Intel integraded graphics.
No matter what kind of graphics you have (dedicated/integrated), the interface you use to interact with them is the same, which is usually OpenGL, Vulkan, and DirectX. There are libraries for those, usually in C/C++, which you'd work with, regardless of whether you have integrated/dedicated graphics. If you're focusing more on general-purpose computing GPU acceleration, you'd use CUDA or OpenCL.
So if you're interested in graphics programming, I'd recommend starting right away :) You already have everything you need.
Buying a different computer is a different issue, and right now chip prices are still pretty high thus I wouldn't recommend buying anything new. Buying used is still a viable option, as you can certainly still find very good deals on Ebay and the like, but if you don't need a new computer at the moment, I recommend just keeping your eye out for a really really good deal, and snatching one up -- it's bound to happen eventually.