My son who is 10 months old is allergic to both soy and dairy. It has been a tough road for him with uncovering his allergies (also strawberries, apricots, watermelon, etc, etc).
He can only have the hypoallergenic hydrolyzed protein formula which is so expensive and he will have until he is two to meet his nutrition requirements. We also feed him mainly fresh veggies, some fruits, and very simple foods made from few ingredients.
I would recommend you continue breastfeeding as long as you can. Obviously traditional formulas are milk based, soy is soy and comes with its own issues, and the hypoallergenic formulas are extremely expensive. Breastfeeding is also shown to reduce allergies and has some protective properties to the gut. As well as the immune properties.
When your daughter stops nursing she will need a source of fat/calories/protein, etc. She will not be able to have milk and soy milk is not as complete as cow's milk and of course human milk. The reason whole milk is recommended at age 1 is for the extra fats, which aren't present in rice or soy milk. It's also because kids fed cow's milk before age 1 are likely to become anemic.
As far as vaccines, I think the only one containing eggs is the flu vaccine. Though you may want to consider not having any vaccines given when the baby is having an outbreak as the immune system is already under stress from the allergy.
It's fairly simple to find recipes that don't need eggs or dairy. You can subsitute soy or rice milk if needed for milk. There are a lot of websites with info on allergies out there that may be helpful also.
Most kids outgrow their allergies, but the key is to totally eliminate exposures.