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As @T4NY4 said try some of the vegan yogurt options. My kids like the soya ones. I don't but the coconut yogurt is ok.
Luckily I drink coffee black, but I think out of all of the mylk options oat is the best in coffee. When we first cut out dairy we had a fridge full of all the different milk alternatives until we settled on the ones we like (some were terrible, so don't get put off if you get a bad one there are loads out there).
i'm thinking having a bit of a transition period, so milk (in coffee) and yoghurt would be ok in the first month, but no eggs or cheese (and no meat/fish of course). This means I basically eat the same breakfast (yoghurt with seeds/nuts/raisins) and lunch (beans/corn/seeds/nuts/salad - just need to replace the egg/cheese) so only have to plan evening meals.