The key is `` by itself. It seems to be a suffix used in child speech and is somewhat analogous to the ~ suffix in the meaning "each other" (Wiktionary). Some examples:
* : staring contest (from {} = stare, glare at)
* {}: washing (somebody else's body); scrubbing each other
* : a children's game with two or more participants (e.g. {} = tag, = playing house, {} = playing soldiers)
It's also seen without this meaning in other child speech or words used to talk to chidren:
* (): pee, wee-wee
* (): hug, hold (a baby)
In your example seems somewhat redundant since already includes that meaning so possibly it was used for a playful or childish tone. It's not specific to Kyoto or Kansai speech. And ~ is just ~ (shall we ~?).