Scientists (including post-docs) are eligible for a TN-1 (I started as one). Out of preference, it may be better to identify your job title as Research Scientist. In a similar situation to yours, I used my Master's degree as proof of education. There was no problem with only a Master's degree in hand. I believe I also had a letter or notification (transcript and the inside cover of my thesis - actually, I lugged my thesis with me) that my degree was within the categories listed among their scientist categories. Under their guidelines, both your job and qualification match the qualification (biologist and animal scientist) so there should not be an issue. My official title was Research Scientist when I started my job (and was listed in the letter of employment I used) and did not pose a problem.

I used the US website and followed their guidelines just to be sure:
http://travel.state.gov/visa/temp/types/types_1274.html

A word of advise, TN-1 are for only 12-months at a time. This may become a hassle and after a few of these, they may suggest that they "can" deny your next request. Once you have a TN-1, it may be better to apply for a J-1 which lasts up to 3 years (as long as you do not have to pay anything) and is intended for Scientists who are training in the US.