While length of the domain is a factor in determining SERPs positions, it is a very minor one. Regular on page optimization and a heavy dose of link building should od the trick.
I am not an expert in SEO, but I know people that are, and as far as I am concerned the length of the domain/site, should not have any effect on its ranking. The ranking is based on the optimization of your site and everything surrounding it like building backlinks, writing and submitting articles, among others.
You can use your industry related keywords in the links of your website. I think this will help to get better results