I'm not a shrimp expert, but a 1g is just barely enough for a Betta. I really wouldn't add anything else until you get a larger, cycled tank. Even in a 1g the added bio load may be too much. From what I know and learned here, I wouldn't recommend adding any more animals into anything less than a 5g.
Edit: And on a side note, if you were able to keep a shrimp in something that small, your Betta may feel that the shrimp is invading it's territory and harass or even kill the shrimp.