Yes, many electrical engineering graduates find excellent opportunities in software development. EE graduates have the advantage of familiarity and a comfort level with hardware that many computer science graduates don't have. Consequently, employers often prefer to train EE graduates for software projects that require a realistic appreciation for what hardware can, and cannot, do. One good way for an EE graduate to break into software engineering is to work at a chip producer, such Intel , Motorola , Xilinx, Altera, or another major manufacturer of chips that are commonly used in embedded systems. Then, having learned the system well for that group of devices, you are in a position to develop electronic systems that use that device.
Some people believe that test engineering is a dead-end kind of a job.
I strongly disagree. The reason is that most new engineers tend to produce designs that cannot be manufactured and tested cost-effectively. First-hand experience as a test engineer will help you to mature as an effective designer, and experienced hirers know this. So, if that's where you are assigned, make the most of it. You CAN move on to other things later.