If you need to, any recipe can be made dairy and gluten free. In this case, it's easy shortbread that can be done in the food processor, adapted from Bluebells Cakery (Random House, 2013) by Karla Goodwin.

2 1/3 c + 1 tbsp flour (I used a GF mix)
1/3 c cornflour
250g butter or non-dairy spread (I used Olivani)
1/2 c + 1 tbsp caster sugar, plus extra for sprinkling
2/3 g crystallised ginger, finely chopped
zest of 1 lemon
zest of 1 orange

Sift flours together in a large bowl or food processor. Rub in butter or add butter and pulse until the mixture resembles find breadcrumbs. Mix in sugar, ginger and zest until a soft dough forms. Wrap dough in a plastic bag and refrigerate until firm enough to roll out without sticking.
Preheat oven to 180C. Line 2 baking sheets with baking paper.
Roll out the dough to about 5mm thick. Cut out shapes with your cookie cutter of choice and place onto your trays about 2cm apart.
Bake for about 15 minutes or until slightly golden; you don't want them to burn around the edges. Remove from the oven and immediately sprinkle caster sugar on top while still warn. Leave to cool on the tray for a few minutes before transferring to a wire rack to cool completely.
If you want to ice your shortbread, just make a mix with icing sugar and lemon juice and ice the biscuits when cooled.