Hi, I agree with FasterPussyCatGrrrl that rice milk is far far nicer than soya milk. We also buy the added calcium variety, but not all versions have added calcium, so it's worth checking the label. If you go to a healthfood shop you might also be able to get other 'milk' alternatives like almond or hazelnut milk (probably best to wait until offering those though, just to avoid nut allergies) quinoa milk (which would be fine to use now but it does taste a bit strange so might take a while to get used to) and one called Tiger White which is made from a cactus.
Re cheese alternatives, I didn't find any very palatable ones either, although this was about 5 yrs ago, so things might have improved since then. Our ds1 is now 6 yo and has goat's cheese but I think the danger is that although many children who react to cow's milk are fine with goat's milk, others aren't. Also watch out with the cheese alternatives as some of them still have some milk proteins in them (which seems a bit crazy to me but I suppose might be useful for people who are only avoiding lactose).
We used hoummous a lot so if you can encourage your little one to enjoy that then it's a good thing to put on sandwiches/crudites/rice cakes etc instead of cheese. Avocado is good too. I found the vegan society website had some good ideas for calcium-rich dairy-free foods (as calcium was the main thing I was concerned about and didn't want him to end up deficient).
From our experience I would say watch out for using too many soya-based products as your little one could develop a soya intolerance if exposed to too much. (I know this doesn't happen to every child weaned onto soya products, but it did with ds1, and there is a link between reactions to cow's milk and reactions to soya.) There are some non-soya 'yoghurt' alternatives in pots called Rice and Rice, although they are quite sweet, and expensive. Also you can just buy pots of fruit puree and use for dessert. If I was feeling up to it I sometimes used to make a dessert myself from eggs, cornflour, rice milk and flavouring, which ends up a bit like set custard but that is quite labour intensive so not what you want at this point .
You can substitute soya milk or rice milk for normal milk in lots of recipes, although you might want to reduce the volume and possibly add a bit of oil to make up for the different fat content. I have made rice pudding and fish pie with coconut milk. Some recipes just don't need the milk and people add them almost out of habit, e.g. scrambled eggs or porridge can be made absolutely fine with no milk in.
And don't forget that at this stage they are just trying things out and their main nutrition is meant to come from their milk (whether formula or breastmilk) until about 1 yr old. So I think it would be okay to just offer her bits of what's on your plate rather than everything, e.g. pieces of cooked veg or potatoes but not the fish pie made with milk. But once I got used to cooking without milk it was fine, and I hardly use any cow's milk now even though ds1 would probably be okay with small amounts. About the only thing it gets used for is dp's cereal and tea!