The difference in resolution between a high end consumer DSLR and a professional DSLR is not that significant. Depending on how big the billboard is and how far away people will view it from, it may or may not be a high enough resolution file.
You can try and simulate it by printing out a file at 300dpi (ideal resolution for close viewing) and holding it at arms length. Stand where you expect people to view the billboard from and hold the picture at arms length. If it covers the billboard, you should probably be ok.
If the resolution is not sufficient, you can either a) take multiple photos with a DSLR and stitch them together or b) get a medium or large format camera that can capture much higher resolutions. There are digital medium format cameras that go up to the 80+ megapixel range, but you would probably need to rent one as they run up in the $50,000+ range. Using a film medium or large format camera is also an option and then drum scanning it.