As I recall, Joey was oily around that age and for a while I gave him twice a week baths, but that really looks like longer than a day. What type of shampoo and conditioner are you using? Biogroom Company will sand you some free samples if you email them. The fluffy puppy might work for you at this age. You should use a cream rinse/conditioner even if they have oily skin, and Biogroom's cream rinse is a light one and won't weigh the hair down. Do you want to grow her hair long? Even if you want to grow her hair long, I think you should get her use to grooming. Her ears need to be tipped and she should have a sanitary grooming and nails clipped. If those are tear stains you might want to try Gerber’s baby water for at least the first year while she’s teething. Gerber’s water has the mineral taken out and helps clear up the tearing problem in some dogs. You can buy a gallon at Walmart for a dollar. Here's a link to Biogroom company, if you want to request free samples.
Bio-Groom - Exceptional Pet Care Products for Over 30 Years Your little girl is adorable though and if she's oily, she has a good chance of being silky, which is so much easier.