My boys didn't use formula, only breastmilk, so we just gave them a cup with organic milk at around 11 months at mealtimes. They readily accepted it because both had a cup from early on since they didn't take bottles, around 4 months we gave them sippies with expressed milk in them.
I think your daughter had problems early on from COWS MILK, not your milk. Did you try cutting dairy out of your diet when you were breastfeeding? Bloody/mucousy stools is a MILK PROTIEN problem, from cows milk in your diet. Very unlikely she had a problem with your milk, it was more than likely something in your diet. If your daughter gets a rash from dairy, its probably a milk PROTEIN allergy. Lactose intolerance is extremely rare in babies and children, and it would be obvious because she would be very sick. I would not advise using soy milk, soy contains estrogen and its just not good for small children, especially boys. Almond milk is a much better option, but again it doesn't contain the adequate amounts of fats her brain needs to develop properly.
Talk to your doctor for his advice, but try giving her small amounts of milk with her formula, and gradually increasing the milk and lessening the formula. It should be a gradual process.