I think it might take about a year. Maybe in the spring when they change coats it will be longer. LH doxies don't really have that long of a coat to start. Is your dog pet or show quality? If pet, it may not get the type of coat a show doxie would have.
I like the LH's better then the SH's - what color is your doxie?
As far as your eating problems, the constant changing to "find what she likes" is making her a picky dog and it will get worse.
Get a top quality food - like Iams, Chicken Soup, Innova (sp?), and not the store brands. And stick to that food. If she doesn't eat it right away, pick it up and put it back down 1/2 hour later. Eventually she will eat it and then start eating it when served.
Unless you have a dog that will eat anything you put in front of them, changing foods and giving table food is not a good thing to get them to eat.