Hi M.,
If you're deciding between binky and diapers, I would ditch the binky first, because once it's gone, it's over and you never know how long the toilet teaching is going to take.
My son had the pacifier at night til around 21 months. When I decided it was time for it to be gone, I just threw them out, no warning. Your daughter is almost a year older so you might tell her, but I would not negotiate or let her know far in advance, I would tell her that day. My son didn't have great verbal skills at that time, but the first couple of nights, he did ask for it and I just ignored the question and he didn't cry. The 3rd night, he asked again and I finally said "You're a big boy now and big boys don't use a pacifier anymore." He gave me a look and I thought he was going to cry! But he just said "Oh," and laid down and I never heard about it again.
Don't stress too much over the toileting. Despite one poster's opinion that the longer you wait, the harder it is, I found that the longer you wait, the shorter time it takes. I had no patience for accidents and being kinda sorta trained so I waited til 3 with my daughter and almost 3 with my son and the process was relatively quick
Good luck!