AngelofGeek, have you heard of the Masuda method? If you breed 2 Pokemon of differing real world origins (like a male Rapidash from Japan with a female Rapidash from Europe) the chances of the offspring being a shiny are increased. It goes from 1/8192 to 1/1365. The 1/8192 statistic applies to all wild encounters, normally bred Pokemon, and special Pokemon (starter, legendary, etc.). So chances are that you'll get one shiny out of 8192 soft resets. Obviously you could get it faster, or even slower, but it's still really rare. The Masuda method would be much faster though. The day care is pretty early in the game too, between the 1st and 2nd gyms, just after you visit the Parfum Palace. So you could get your shiny there, easily train it up to your team's level with how awesome exp share is now, then just have it replace the one you first got.
Most people just get a foreign Ditto from the GTS or from someone on the internet. Other benefits to breeding for a shiny include being able to guarantee the nature of your Pokemon, pass down egg moves, and even get the hidden ability on your shiny, providing the mother has the hidden ability. To guarantee the shiny Pokemon's nature, use a parent that has the nature you want (so if you want modest, breed for a modest Fennekin first) and have that parent hold an everstone in the day care. It was changed this gen to have a 100% chance of passing the nature down to the offspring, rather than 50% like previous gens. Then get a Pokemon with the ability Flame Body (the new fire bird works) or Magma Armor since they halve the steps needed to hatch eggs if they're in your party.