We were very lucky and never had many tantrums around here, so I don't know if my ideas will be helpful at all, but thought I'd toss them into the mix, anyway (as well as welcome you to the group, doctorbighands--welcome!).
I wonder about sensitivities: none of my boys could stand tags in clothes, seams in socks, or synthetic fibres when they were babes and toddlers--something to try?
Also, at nine months, I'm thinking teeth, maybe? Could be that she just plain hurts.
One thing that worked really well for all of my kids was giving them choices all the time, even well before they could talk: do you want the blue shirt or the orange one? shall we put the left sock on first or the right one? would you like to use this spoon or that one? and so on. There are no wrong answers to these kinds of questions! (Even if it's "I choose to eat with both of the spoons at the same time, Mummy"!) It's nice for them to have a bit of control. For the same sort of reasons, I used to have them help me with things (bringing me a book or combing my hair or something like that).
We also "taught" them a lot when they were small (not with any intention of hothousing, you understand, but just in the sense of sharing bits of the world with them): I'd take a tree book to the forest with them, we'd stroll over to a tree, feel the bark, crush some needles between our fingers and smell them, show them the picture of that species in the book, tell them the name of the tree, then go find another. Same for birds, bugs, seashore creatures, and so on. (Outdoors time was--and is--really big for us: when people were getting a bit cranky generally, I tried to get us out into nature and cheered up.)
Or I'd take them to an office building with a lot of stairs (at a quiet time of the day), and we'd climb and count stairs, over and over (good for my fitness level anyway!). I do remember that one of my boys particularly insisted on the counting (we had to go back down and start over if I forgot to count out loud), so it wasn't just the steps, I don't think.
All of my kids liked watching me cook from their highchair. I'd bring ingredients over to them, tell them what I was making and what I was going to do next, let them smell spices while I named them, and basically kept up an informative monologue as though I were doing a cooking show on TV. I did this with lots of stuff--basically a running commentary on the routine tasks of the day.
I also remember bringing them scraps of different fabrics to feel and describing what they were: velvet, corduroy, silk, linen, denim--they all feel different and interesting to a baby, and some kids are really tactile learners.
Well, I'm veering way off topic now--but I guess my point, if I do in fact have one, is that sometimes frustration stems from inability to communicate, as of course you already know; and we found that with our kids, giving tons of choices, supplying lots of informational input, and talking to them as though they could understand perfectly well what we were saying seemed to avert quite a lot of that frustration. My sample size is three, however, so not necessarily much use to you.
You're doing just fine--all will be well!
peace
minnie
