Sounds like products marked 'vegan' would be the best way to go for your for now. These will eliminate most of your intolerances straight away. I am sure that you already read every label before buying.
I have been dairy free for 10 years (intolerant) and serve a dairy free diet to my DS (who has had full milk allergy since birth). Many people live without dairy and thankfully substitutes are very well developed. It is good that you have been referred to a dietician. They should be able to give you lists of substitute products, cookery ideas and many can prescribe dairy replacers and vitamin supplements for yourself and baby. They are also very good at discussing any anxieties you have about you/your baby being on a restricted diet. Cooking with diary free does sometimes require some trial and error e.g. if it gets too hot it can curdle.
Should you choose to go onto bottle feeding; they can prescribe Nutramigen/another formula for baby so that you can get it for free. Like LAF suggests the dairy free formulas tend to smell and taste different (Nutramigen is almost savoury in flavour) but it was a god send to me after 18 months of pukey baby and sleeplessness.
I think soy products are the closest match to cow's milk but oat milks are also available. Many soy products have some vitamin/calcium enrichment. The milks are all good in tea and coffee - so you can still get your caffeine fix!
These are worth a try...
Alpro soy milks, yoghurts, creams, milkshakes, custards etc (widely available and creamy)
Provamel soy (very yummy and have some interesting flavours)
Viva Soy
Holland and Barrett's own soya milk (often on manager's special)
Mark's and Spencer Soya Drink (top creaminess - lovely)
Benecol Dairy Free probiotic drinks
Vitalite Dairy Free Spread
Pure Diary Free Spread
Swedish Glace Ice cream
Freedom Ice Cream
Any Dairy Free Chocolate with Carob in (bitter and strong - great if you like you chocolate dark, but can also be mixed with milk substitutes).
Asda Dairy Free Buttons (closest to milk chocolate I have found)
Like another poster; I have not found a decent replacement for cheese though. I have tried a few brands but some can either taste very rubbery or chalky.
You can make decent food/ have nice snacks on dairy free - so please don't panic too much. If you need anything else just shout out.