Here are some tried and tested egg free recipes which might help
Mini Banana muffins (taken from veganfamily.co.uk)
200g./7 oz/1 and a half cups of white flour
50g./2oz/third of a cup of caster sugar
1 and a half tea spoons of baking powder
3 fl oz/100ml of orange juice
3 fl.oz/100ml of sunflower oil
2 mashed bananas (over ripe is best)
some milk as required
vanilla essence
dash of vinegar
Combine the dry ingredients in a bowl. Mix the wet ingredients - but not the vinegar - in a jug or bowl. Mix the two together and then stir in enough soya milk to make a smooth mixture and add the bananas, Finally add the dash of vinegarand mix well. This should make enough to fill about 40 mini cake cases. It's a good idea to put them in a muffin or patty tin to help them keep their shape but not totally essential. Bake for 10 - 15 minutes at 190 degrees and then cool. These freeze really well so can be made a week or so ahead and just taken out of the freezer an hour or 2 before the party.
Or try this www.bbc.co.uk/cbbc/bluepeter/active/bakes/bake_partycake.shtml but make it in a square tin and cut into fingers or squares when cool - most digestive biscuits are free of egg but may need to double check to make sure
or what about the good old rice krispie chocolate things - I have a recipe if you need it.
Have some more recipes if you need them - dd is egg and milk free so have an armful of tried and tested quick and easy vegan treats!!