I would recommend purchasing a device like this anti dog alarm: http://www.amazon.co.uk/gp/aw/d/B0051GO5...X110_SY165
I hate the idea of a dog attacking my daughter so we added one of these to the nappy bag and continue to carry it when in parks etc.
I've only had to use it once (on holiday) and it repelled the dog without the need for a good kicking.

there is a specific picnic area in the park, next to the playground that is enclosed by a fence.