I have been learning about Blender and graphic design for about 6 months, but I feel like my standard desktop computer is holding me back.
How much of an impact is the performance of my computer affecting my learning?
How much faster would I learn if I had a proper graphics workstation?
Without posting the specs of your computer we have no idea what sort of improvement you will see.
That being said… I doubt it will help you as much as you think… sure it will help a bit but there is a lot you can learn whilst using a low powered computer.
Your hardware should have no impact on your learning ability. If anything, my laggy laptop taught me to optimize my Blender scenes in ways I wouldn’t have thought of otherwise.
That said a faster workstation always helps for actual work and less stress so if you can afford it, go for a new one.
I’ve found there are two main factors when dealing with hardware for graphic design—available RAM and GPU. When starting out a computer with 2 or 4GB of RAM will suffice, but I’ve dealt with large files that end up choking my 4GB laptop. The moment you start dealing with production-level work I’d recommend upgrading to 8 or 16GB.
The choice of GPU simply comes down to the software you use and how much money you have to spend. For a Blender computer on a budget, I recommend the Nvidia 560ti—it’s the “younger brother” of the 580, with a similar performance at about half the price. The 580 is a great GPU for Blender, but there are many others that will work just as well. Here’s a great reference for GPU benchmarks: http://benchmark.cd3dtech.com/Benchmark/benchmark.html.
Note that a lot of graphics software does not allow for GPU acceleration, despite its growing popularity, so be sure to choose a powerful GPU only if you know you’ll be able to use it. Otherwise, make sure you have a solid processor and plenty of RAM. 
I think I’d agree with what’s been said here, mostly. In my opinion, upgrades on things like CPU, GPU, and RAM are more “efficiency” tweaks. In other words, they’re things you can do to handle bigger scenes, faster renders, and things like that. There are other things you can do that will improve the quality of your work that are much less expensive and can be done, even if you have a weaker system.
One of the best things you can do to start improving the quality of your work is to learn to work from references. Whether this is a modeling sheet for a character, or photos of objects you want to create, or even taking something around the house and grabbing a tape measure. These sorts of things will go a long way to improving your skill, even if you have a slow machine. Also, if you want to do any sculpting in Blender, I’d recommend getting a graphics tablet, like one of the ones from Wacom. Getting things like a mirror, a tape measure, and a Wacom tablet can be less expensive than the system upgrades and will really do more to help you improve your skill.
I know everyone mentions upgrading the GPU and RAM when it comes to getting faster renders, but don’t neglect the CPU. As new features are added into Blender Cycles, they’re often not available on GPU at first. And there are some scenes where it could be possible that the GPU can’t handle what you want to give it. But again, I wouldn’t worry about any of these three at first.
I’m working primarily off of a laptop, which limits my resources, but I’m still finding it more than capable, if somewhat slowly, of handling most of the things that I throw at it.
Everything said previously covers the hardware. Assuming you’re not running into a situation where you simply cannot render something due to lack of resources (if it’s due to GPU limits, there’s no shame falling back to the CPU… there are features that require that currently anyway), are you possibly prematurely rendering in high quality/resolution? You want things to be as interactive as possible while you are figuring things out / iterating / learning. Dialing back both the quality and resolution while you’re still figuring a scene out should be able to more than counteract any system performance issues. As you approach your final render, start dialing things back up as needed and do your final render while you sleep. But sure, if money is no object more/better/faster hardware is the more fun solution