A.B.
My son was very similar at 1. Around 15 months we started to wean because we were going to try to get pregnant - I hadn't had my period that entire 15 months due to breast feeding and birth control!
Anyway, by 15 months, my son had already dropped his daytime feedings so we just had to drop the morning and bedtime feedings. The morning was super easy because my husband just took him in the morning and gave him a sippy of milk with his breakfast. The bedtime one was harder - but just on me! Again my husband took over the bedtime routine and rocked my son with a sippy of milk - we used up my frozen breast milk before bringing in regular milk - and he was completely weaned by 16 months.
We took it slowly and followed his cues for the most part - he was just ready at the time so we didn't have any drama at all - which truth be told was upsetting to me - didn't he miss our special time together the way I did? But then I realized that instead of nursing, we had more time to snuggle up with stories or just rock in a chair while listening to some music.
Like everyone else has said, you just need to follow your own heart and do what works best for your family. I think at one, kids are starting to gain a lot of independence when they get mobile and that's probably a little scary. My son took the paci and has a special lovely so he was able to self-soothe during the day when he was transitioning so it doesn't surprise me that your daughter is being soothed by breast feeding :)
Best of luck on whatever you decide :)