Here is a simple recipe:

2 cups self-raising flour, sifted
3/4 cup caster sugar
3/4 cup milk
125g butter, melted, cooled
2 eggs, beaten
1 teaspoon vanilla essence

Icing
1 1/2 cups pure icing sugar
food colouring, optional
1 to 1 1/2 tablespoons water

Method
Preheat oven to 200?C. Grease a 12 x 1/3-cup capacity muffin pan. Alternatively, line holes with paper cases. Combine flour and caster sugar in a bowl. Make a well in the centre.
Add milk, butter, eggs and vanilla to flour mixture. Using a large metal spoon, stir gently to combine.
Spoon mixture into prepared muffin pan. Bake for 12 to 15 minutes, or until a skewer inserted into the centre comes out clean. Stand in pan for 5 minutes before transferring to a wire rack to cool.
Make icing: Sift icing sugar into a bowl. Add food colouring and water. Stir until smooth and well combined. Spoon icing over cupcakes. Decorate with sprinkles and lollies.

I have another one that is much more time consuming but makes much softer fluffier cakes but given your purpose I don't think it is worth it. Kids just love any cakes esp with icing and lollies on top.

OR
Tiny Teddy cupcakes from taste.com:
125g butter, at room temperature
155g (3/4 cup) caster sugar
2 eggs
1 tsp vanilla essence
200g (1 1/3 cups) self-raising flour
50g (1/2 cup) cocoa powder
185ml (3/4 cup) milk
16 Arnott's Tiny Teddy chocolate biscuits

Buttercream tinted with tablespoon of cocoa in 1/2 tablespoon hot water

Method
Preheat oven to 180?C. Line sixteen 125ml (1/2-cup) capacity muffin pans with paper cases. Use an electric beater to beat the butter and sugar in a bowl until pale and creamy. Add eggs, 1 at a time, beating well after each addition. Stir in the vanilla. Fold in the flour and cocoa, alternately with the milk, until combined.
Spoon the mixture among paper cases. Bake for 15 minutes or until a skewer inserted into centres comes out clean. Set aside for 5 minutes to cool before turning onto a wire rack to cool completely.
Spread 2 teaspoons of icing over each cupcake. Set aside for 30 minutes to set. Top cupcakes with biscuits to serve.

With your Barbie cake you can always buy two boxes of vanilla cake mix for the base? Do you have a Dolly Varden tin? It is worth hiring one (about $5) to get the proprtions right. And break of Barbie's legs and just push her hips into the cake to save splitting the cake. You can put the legs back on later if you are kind (I wasn't!). I made a dolly cake for my DD in Dec but it was a choc mud cake with pink buttercream icing. If you are using the proper tin you will need larger quantities of mixture that the cupcakes. If you hire it ask the hire shop ladies how many packets of cake mix you will need.