Hi A.,
I remember feeling the same way when my daughter was 10 months old. I was ready to wean within the next month or two and she just seemed to become more and more attached to breastfeeding. I felt a bit of panic about it. But, I have good news for you. Just because your daughter seems like she can't get over certain things without breastfeeding doesn't mean that you will have to nurse her until she's 15. It just feels that way.
She gets a lot out of her nursing relationship with you. She feels warm, comforted, and gets actual nourishment from it, so it's only natural that she would feel attached to your breasts.
I wouldn't worry about supplementing with formula and weaning her completely before a year old. You're so close to the year mark, why not continue to nurse until 12 months - then you can put her straight onto milk from a sippy cup - I guess I'm a lazy mother, but I hated making formula, plus it smells gross. I weaned my daughter at 13 months, we started the process just after she turned a year. Up until then, I nursed her on demand - including when she was upset.
When we started the weaning process, I looked at a calendar and marked the dates I would drop certain feedings. First, I stopped nursing her when she got herself upset, I actually did that around 11 1/2 months. I would take her for a walk, I would hold her tight and kiss her face, and eventually she stopped expecting to nurse when she was worked up. It's hard, but once she figures out that she can soothe herself and you don't give in and breastfeed, you'll be surprised how quickly she gets used to it.
Then, I dropped any feedings that weren't upon waking. So, she still got to nurse in the morning, after her morning nap, after her afternoon nap, and before she went to bed at night. I didn't replace those feedings with milk, I just started offering more quantity and variety of foods at mealtimes, making sure that the foods were fresh, nutritious and high in fats (like avocado!) I allowed her about a week to get used to that routine and then, every five days or so, I would drop a waking feeding and replace it with milk.
She wouldn't take cow's milk at first, so I put a little (about an oz) of pediasure in the bottom of the sippy cup and would fill the rest of the cup with whole milk. The sweetness of the pediasure made her LOVE milk. After about two weeks, I dropped the pediasure and she is still obsessed with her milky at 18 months. While she was on the small amount (about 4 oz a day) of pediasure her appetite went down - just an FYI - but she got it right back when I stopped putting it in there.
She responded really well to the whole process. She seemed to make some major developmental leaps after we finished weaning, as though she had been waiting to stop nursing to do it. She walked the day after I dropped the last feeding. Probably a coincidence, but funny anyway.
Whatever you decide, remember, you are the expert on your child. No one knows better than you what is right for your child or your family. When it gets difficult, think about how you feel about the decisions you're making, and then do what's right for you. 10 months was around the time that a lot of mothers I know started getting criticism from non-nursing family members and questions like "when are you going to wean her?" in a critical tone of voice. Those people aren't your daughter's mother. Their decisions were right for them, and that's great, but you don't have to do it the same way.
If you do decide to nurse your daughter well into her first year, there is nothing NOTHING wrong with that. There is no right or wrong time to wean. Just make your decision for yourself and your daughter and it will all come out okay. I guess the key is being comfortable with what you want to do, and having faith that you're doing the right thing.
Good luck.