The other answers here offer some great insight and ideas for learning to develop. I’d like to add an additional piece of advice about actually “making the jump.” At my current job I was originally hired as a GIS tech mostly doing basic drafting, data entry, and routine analysis. Much of the work was tedious and repetitive and the more I work I did, the more areas I noticed could use some improvement. So over time, I started writing code here and there to help speed things up or automate them. I started sharing these tools with other employees and asking what else they thought might be useful. It wasn’t long until my supervisors noticed and started shifting my responsibilities toward application development. Ultimately my position was reclassified and now my primary responsibilities are creating desktop and web applications for the department.
In your position, my advice would be to start creating scripts and tools and share them with others around you. Use the information others have given here to broaden your development skills so that you can offer increasingly more powerful solutions to your coworkers. Over time, your services as a developer will become more in demand as they have a positive influence on productivity of your workplace. And while this may not result in a change at your current job, you’ll still be getting solid experience that can translate into another job down the road - one that is perhaps more developer oriented.