With my older son, I waited until the traditional 2.5 age to potty train him, and it was not so bad, only took a few months, and before age three was potty trained, but the hardest part was getting him to poop on the potty (it was quite a battle of wills). So, with baby number two (both boys) I decided to go a different route and get him pooping in the potty ASAP before he was old enough to know any different. I began potty training him at 15 months, despite others telling me it was too early. He just turned 2 last week and, surprise surprise, he is potty trained. I have not changed a poopy diaper in MONTHS, and it is wonderful!
This is what I did, and what I recommend at that age: Since bowel movements are often more predictable (or at least more noticeable) than urination, start with that. Start tracking the time each day when she normally has a bowel movement (if you already know that...even better)and after a few days, put her on the potty around the time she would normally poop. If she does nothing after five minutes, wash up and be done with it and try again tomorrow. If you are consistent with it, eventually she might just poop in the potty by "accident" and when she does, you should make a REALLY big deal about it...sing the potty song, dance, high five, tell her what a big girl she is, wave bye-bye to the poopy, etc. On the same token, WHENEVER you notice any telltale signs that she is about to have a bowel movement (the poopy face, suddenly becoming very quite, grunting, whatever) rush her to the potty RIGHT AWAY, likely there will not be any poop in her diaper yet if you catch it soon enough, but even if there is, have her finish on the potty, and then, same thing, LOTS of praise and excitement.
At that age, a BM rarely happens with out urination, so it is natural for it to follow suit. Once you have the poopy down, begin putting her on the potty for pee pee about every two to three hours. The key is you have to be consistent. Once you start, don't stop, even if it seems like she is not getting it. I noticed with my son, once we were consistent with potty every three hours, he knew when to expect it, and he was staying dry. He began right away telling me when he had to poop, but it took a few months before he was telling me when he had to pee. Also, putting her on the potty first thing in the morning is very important, even if she is already wet. When my son knew to expect the potty first thing in the a.m., he began staying dry at night (right around 18 months).
BTW, I never used the little potty chair, just a sturdy step stool and the big potty (I just did not want to clean poop out of that thing...grosses me out). But whichever you choose should be fine.
Also, doing it this way, I never had to use treats or bribes like I did with my older one, becasue he never knew any different...the verbal praise was its own reward at that age.
All that being said...keep in mind that all kids are different, and I would not expect that this would work for everyone, so keep an open mind and it may take trial and error to find what works best for your daughter.
I just want to add that I NEVER forced my son...he actually enjoyed pooping in the potty and after just a few days was telling me when he had to go, and was completely able to control it, so it is possible at that age, and it can't hurt to try. When I started I did not expect him to be potty trained any time soon, I just wnated to get him used to pooping on the potty, and to my surprise he pick up on it on his own very well.