Question
The main option I see is re-direct the domain to my site. However, my uneducated guess is that Google will probably de-rank the domain pretty quickly if I do that.
Looking for some expert opinions.
Answer
It depends, if all the organic traffic is going to the home page and your domain target the same topic, you woud probably transfer the ranking. If there are lots of pages ranking on the domain you bought, you would need to offer the same content on your site and redirect url by url!