Can someone else get a patent for our invention?

The prior response is correct regarding first-to-file. You could, however, file a provisional application for the invention, which remains unpublished, and gives you one year before you need to file a non-provisional application. A non-provisional application is published at 18 months unless a nonpublication request is submitted. Therefore, you could get protection for your invention from later filers and have the invention remain unpublished for 30 months or more.

AS of March, 2013, the USPTO went to a first-to-file system as opposed to the previous first-to-invent system. Under the previous first-to-invent system, an inventor who file second might prevail if they could in fact provide evidence and prove that they were the first to conceive and effectively reduce the invention to practice - this was all accomplished through means of an Interference proceeding. Under the current first-to-file system, the inventor who is first to file his patent application in the USPTO is now the senior inventor, meaning, their application would be considered senior to your patent application, if you filed one at this date, and meaning, furthermore,
that their patent application would be considered to be prior art with respect to your patent application and would therefore effectively prevent you from obtaining a patent. Assuming that the first party obtained their patent, they would have a valid right to prevent you from making, using, and selling your invention here in the US.