Whenever you hold a human being by an appendage or 2 and then whirl them around, you create substantial force on their body, proportional to the rotational velocity at which you are spinning them. While this can be done at various ages, declaring it as "safe" is a non-starter. Any number of odd events could happen causing you to lose sufficient focus on the task at hand and jeopardize her safety (I'm not saying you would willingly do that b/c if you're like me, I'd hurt myself well before allowing my daughter to be hurt!), but "accident" isn't about the planned.
Now, all that security warning ahead, I'd say you can kind-of get away with it at a year or so, but the real question is at what age you shouldn't do it (wouldn't want someone doing that to you now, right? lol!) I used to let my daughter climb up the front of me and flip over backwards (best description I can think of for it, so hope you have an idea of what I mean). That stopped when she got big enough that I wasn't 100% sure of my balance (and hence her safety).
Final comment from a hyper-cautious parent: Don't forget that angular motion moves everything in the body outward, so the brain gets pushed out against the skull (depending on the strength of rotational force), too. Just be very, very, very careful if you find you must do this.