Well eevee is a fox, not really a dog. But if there had to be one, in my opinion, I would say a German Shephard puppy. There might be a better answer but this is my guess.
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Take Eevee to the daycare center with another Pokemon. And make sure that these Pokemon are compatible with each other. Such as Eevee/Ditto, or Eevee/Eevee. You should also try breeding Eevee with other Pokemon to see if there compatible or not. If they 'get along or don't like each other much' you get an egg. If they play with more Pokemon then each other try another Pokemon because you won't be getting another Pokemon.
Try the Masuda Method. Get Ditto from Japan and breed it with the Eevee. It increases the chances of it being shiny. Alternately, there may be an Action Replay code to do something like this.
hi unknown k looks like a k
Unfortunately, once evolved eevee can't evolve so sorry but for now you're stuck with leafeonnot necessarily. if you have another eevee that is a different gender from your leafeon or you have a diddo, you can breed them in the Pokemon daycare center and try again.
The Pokemon that looks like a acorn is Seedot. There's a Pokemon that looks like a pine-cone called Pineco. In addition there's a Pokemon called Ferroseed that is based on the spiky cocklebur.