You can get into a lot of quality for $1,000. You just need to pick the right tools for the job.
First: by outdoor activities, do you mean recording your hunt by yourself, necessitating portability (such as a GoPro) or having a dedicated assistant who can dedicate 1-2 hands to a more complicated setup?
Also: how much weather will it be exposed to? Most Canon and Nikon DSLRs have sucky weather sealing so that rules most of them out.