I highly recommend the book put out by the Le Leche League about weaning... I think it is called 'How Weaning Happens'. It is possible that her metabolism is high, therefore her tummy empties quicker than others and she needs to nurse at night when no other food is being offered. Is she really eating or just licking and playing? I assume at 1 yr, she is really eating, which means she needs it. Lactation consultants told me that if they actually eat, then their body is hungry and telling them to eat....taking it away, especially at night may be very challenging :-)
If you are wanting to make the process happen before your daughter is showing that she is ready (reducing the nursings on her own) it is best to be slow and gradual....this way it is less stressful for both of you and keeps that special bond you have made strong and keeps that trust that she knows between you. Right now she turns to you not just for the extra nutrition and health benefits, but also for the emotional comfort that she needs. Every child is different and it sounds like your daughter is similar to mine in needing extra comfort a little more often than a different kid of the same age. My daughter also nursed several times a day and all night until she was about 18 months old. She still continued to nurse but requested less often for a while. Although child led weaning is much easier for the child, it is true that if YOU are getting aggravated about having to nurse, then it is no longer a mutually desired event and you should consider weaning, at least partially to ease your frustration. At the Morton Plant nursing moms group, the hospital lactation consultant says that the way to wean is to 'make your nursing box smaller' meaning to start with taking away one nursing (the one that she will miss the least and fuss the least!) every month or so (whatever is comfortable for her).... continue to take one nursing away at a time until you are left with only a few, a couple, or just one that you can live with until they give that up too (or you take it away).
Try LOTS of distrations-keeping in mind that her nursing is not entirely about being thirsty or hungry, so offering a different drink in a sippy may make her more frustrated and confused - or it may be enough to distract her. Alot of what she desires is the special closeness she shares with you while nirsing and may have a hard time understanding why you don't want that too, and may also have a hard time accepting alternatives, especially since at a young 1 yr old, she doesn't comprehend alot of reasoning and explanations yet. Maybe cuddle time, reading stories will work or it might remind her too much of nursing and Daddy may have to hold her, rock her, take her to bed etc instead. I would guess that night weaning will be hardest, and the most disruptive to everyones sleep...so you may want to save that for last after she has conquered some reductions in the day nursings. You may decide to keep the night nursing all together to save some special bonding time just for her? Keep in mind that she's only one and most children will nurse longe than one if given the chance....(recommended by WHO till age 2), so be prepared for some changes in her as she tries to comprehend why she can't nurse. She may get more clingy, upset, change sleep/nap patterns, show stress since her comfort has been changed/removed. It has been what relaxes her and draws her into you, so maybe a strong alternative to connect and support her needs will be helpful?? I am a firm believer that the breastmilk that I gave my daughter sfter age 1 helped her health and development in ways I couldn't measure - especially emotionally. Hopefully you will find a happy medium with your daughter and keep you both happy and secure. Congrats on being an awesome mom and for choosing to nurse, giving her the very best nutrition, comfort and security you could ever offer her! Best wishes....