i love my pump. i can make changes in much quicker time. for instance, last night i was nervous about my first day at a new job today, and the adrenaline was pushing my BG up. I noticed it, and then i just upped my basal rate by 20% for the next two hours until I would be asleep. With MDI, I would have had to take a shot of humalog, which would have put around 2 units in my body and sent me low and then rebounding back up.
I can lower the basal rate for exercise or alcohol. I can now eat foods with good control that i could not on mdi, like bagels, muffins, pasta, cereal...
I have refused to by pocketless clothes since well before i was diabetic, so getting another electronic into my back pockets is not a big deal for me. the most annoying thing is lowering my pants to change clothes or go to the bathroom, but I either do the tubing yoga and it's okay, or I just disconnect really quickly.
on mdi, i was forced to eat to feed lows often. i couldn't skip meals (i was on lantus and humalog, but it just didn't work out.) without going low. i lost my sensitivity to lows - i would be 32 and have no idea, just barely noticing that the hill was harder to climb on my bike than usual.
on my pump, i can go all day without eating. if i start to rise because my liver is kicking out sugar, i can correct that easily. the IOB feature makes me way less likely to stack insulin and get the scary lows i was getting on mdi.
but the immediate and huge difference for me was that all of a sudden i could eat fruit again. I didn't have to decide whether it was worth the shot and then try to draw up a half unit of insulin in order to eat an apple. it made me feel like diabetes what something there, a part of me, that i deal with, but that isn't all or even most of me.
CGMs are really useful tools but can be maddeningly frustrating. Also, I don't think a CGM would have helped me on MDI much at all. I use it mostly for detecting lows before they happen, so that I can drop my basal rates and not have to feed the low; and for figuring out basal rate changes - which you can't do with shots. If you just want it for hypo unawareness or for alerting to highs earlier, then by all means, go for it. But if you had to choose between a pump or a cgm, i'd recommend a pump 300%. I believe a pump will help her control much more than cgm will.
Of course, pumps aren't for everyone, but if your daughter wants one and thinks she is ready, i say go for it. If it doesn't work out, it doesn't work out, no harm no foul. But if it does, it might be a huge step forward in her diabetes management.
Good luck with the decision.