I've been in your position and I'm one of the few testers who has come out the other end with a Design job (becoming increasingly harder), and here's my advice for you;
Your location can have a massive impact on your options. The majority of testing has been moved from in-house teams to massive low cost test centers in Romania or India, and that's where all the work has gone. In most cases a junior tester either needs to already live next door to a studio or have a mate already working there to vouch for them. Even then those jobs are harder to find because testers are precious about their jobs, and unless they're offered something better they will never leave.
Once you have a testing job that's only half the battle. The other half is moving from QA to Development without stepping on toes. QA testers can be very volatile and unforgiving if you burn them or if they feel you cheated them out of the design job they applied for too. Prove your value and earn their respect when you're in the trenches with them, and you'll soon find you've got an army of testers on your side in your design role.
One last thing, if I could go back in time and repeat university I would either take up an animation or a c++ course. The knowledge you gain from those courses is invaluable, and if you are struggling to find a job in games, those skills will get you a decent job outside the industry.