I have two concerns with using Scrum on this project.
First, the team size is too small. Scrum recommends having a team of 5-9 people. With only 3 people, you are significantly below that recommended size. Also, a key role in Scrum is the Product Owner, and you don't mention someone acting in this role.
Second, you have what appears to be a deadline, where the project will conclude in 3-4 months. Scrum (and other iterative and incremental methodologies) works best when you have a flexible window with with to work. The idea is that you very quickly get to a point where you can determine what features you can implement in a 2-4 week increment and the Product Owner is capable of prioritizing features and stopping development as soon as the cost of implementing another set of features outweighs the value added by those features.
I think that you can take lessons from Scrum and other agile methodologies, but I'm not sure of vanilla, out-of-the-box Scrum is appropriate in this environment. 15 minute daily standups, using a product backlog, continuous integration, TDD, and other agile practices would be worth looking into, but I would tailor the process to work for this project.