Yes, we've experienced tantrums from a very young age. I would first like to say that I come at this from a different perspective. I would never say DD is trying to manipulate me or is trying to be obnoxious but rather that she is trying to express her frustrations at whatever the situation is but lacks the words to explain that or the knowledge to understand why things are happening in a certain way.
So coming from that perspective here's what we do. Prevention is best. Make sure your kid has enough sleep, isn't hungry, isn't bored, isn't being ignored etc. If there is something you know is going to set off your kid just try and avoid it (around 6 months DD was deathly afraid of a certain toy and would freak out when she saw it so we just avoided showing it to her or would try and introduce it to her very gently so she would know it wouldn't hurt her). Also some toys when taken away ALWAYS caused a tantrum so we either didn't introduce them to her too often or tried to prepare a very, very good distraction when they needed to be taken away.
FWIW, I think 9 months is WAY too young for time outs. Actually, I tend to believe time-outs are rather ineffective and I don't like the philosophy that separation from parents is a punishment (especially since we already had a number of issues with separation anxiety at that age). Why are you putting her in time outs? Does she understand the reason behind it? I've always heard that it's supposed to be a minute for ever year of age so under a year is too young...
Honestly, if you're dealing with a gifted child the easiest thing on everyone involved if following their lead. Provide a safe baby-proofed environment where your child can explore and there's not many things that she would need to be corrected on. Our apt is proofed to the nth degree. Granted, DD figured out how to get into a number of things very early on (all those electrical socket covers came off immediately!) so we rearranged a lot of furniture/toys so they weren't in her line of site.
The one exception was the cat's litter box, it's in the bathroom and we started putting her on the potty at 9 months so it was an issue. We just never let her walk by it so she learned pretty quickly that we always picked her up and carried her past that part of the bathroom. Once she figured that out we let her walk by and just made it clear she shouldn't go near it and she never dos now.
I'd also suggest to look at what your daughter is trying to tell and don't put age expectations on her (especially if she is advanced). We really had to think outside of the box with DD to help with her tantrums (like early potty training, moving her out of a crib/pack and play very early on, etc.) but things got soooo much better once we followed her lead instead of trying to do the "age appropriate" thing that every recommends.
I also wanted to add that you might want to look into baby signing. It's helped DD a lot. Unfortunately, she's hit somewhat of a road block because of her fine motor skills but she's knows a lot of signs and will use them to communicate with me.
