I do know somebody who's DD was trained before she could talk much - as you describe it was led by the child, who also said "wee" no matter whether she wanted to wee or poo and who had only a handful of single words. My older 2 children were talking in sentences by 2 but not ready to potty train until 2 and a half (DD), and 2 and 3/4 (DS1), but at those ages they both did it in a couple of days with only a couple of accidents - my youngest is 23 months with pretty good language (sentences) but is also not yet ready to potty train and not interested in doing so. I also know somebody who tried to potty train at not quite 2 because she thought her DD must be ready due to reasonable language, and she ended up spending over a year "training" her, with multiple accidents daily the whole time - which seems mad to me! I don't think potty training readiness is directly linked to language, although of course having enough language to say what they need makes it easier!
I'd say give it a go if she's interested, but don't get hung up on it and make work and stress for yourself and her - if she's ready she'll do it pretty easily without too many accidents, there is really no point in persisting at this age if you are cleaning up multiple accidents per day for more than a few days in a row - no harm in a gentle child led try if you are up for it, but putting her back in nappies for at least another couple of months if it doesn't click.
If you think she is ready and showing in interest, then I would begin potty training. I did a sticker chart for my DCs and it worked a treat. If they managed to do a wee/poo in the potty, they would get 1 sticker for a wee and 2 for a poo. They really loved stickers, so this was a motivation for them. ( Poos in potty took a bit longer to get the hang of)
Then when the end of the chart was reached, they got a new toy to say well done. (Our chart was 60 stickers long).
My DD is 24mo and still mostly babbles, have lots of words, but very few two word sentences. At her 2 year review last week, the HV advises to start potty training at around 2 1/2, based on her language ability. But two days ago, she suddenly said wee wee, wee wee and went and pointed at our toilet. We put her on it and she sat there until she pooed. We went to buy a toilet trainer that day.
Since then she has been obsessed about the wee wee as she calls the toilet. Unless she is busy, she keeps asking us to take off her clothes and sits on the toilet. It's basically her new game. But mostly she is not peeing or pooing, just standing up and sitting down on the stool, and playing with her soft toys. She has managed twice to do it on the bathroom floor. Once before a bath so we don't know what she was really doing before. Another time she climbed down the stool but refused to put her nappy back on, then proceed to quickly gave that stare and a poo. She is happy to put her nappy back on when she has finished her toilet play.
Sorry for the long post. But I'm not sure how good her bladder control really is. If she still don't even tell us she has pooed in her nappy yesterday, surely she can't be toilet trained? Or should I really be starting it properly as she has indicated strongly she wanted to?