Can I let my daughter own a dog?

Islam gives permission to keep dogs for certain purposes, such as hunting, guarding livestock and protecting crops.The only thing that it is considered haraam in Islam is to grew up the dog inside the house because of its saliva. The saliva of dogs often contains microscopic worms, science has shown. Dogs are not to be kept inside the house at all times. They should be kept outside. below are the thing considered haram about dogs:

• eating dogs meat
• touching dogs feces
• keeping dogs in your house and living with it
• if a wet cloth contact with dog,you can't pray in that cloth and you should wash and clean it completely. Even if the dogs fur was on your cloth it is considered unclean and you should do the above mentioned

and one of the reason for that is because dogs and pigs have numerous microbes and are dirty.
The other reason is because they don't let angels come into your house

It is a fundamental tenet of Islam that everything is permissible, except those things that have been explicitly banned. Based on this, most Muslims would agree that it is permissible to have a dog for the purpose of security, hunting, farming, or service to the disabled. Many Muslims strike a middle ground about dogs -- allowing them for the purposes listed, but ensuring that the animals have their own space which does not overlap with human living spaces. Many would ensure that the dog is kept outdoors as much as possible, and at the very least is not allowed in areas where Muslims in the home pray. For hygienic reasons, when an individual comes into contact with dog saliva, one needs to wash.
Owning a pet is a huge responsibility, that Muslims will need to answer for on the Day of Judgment. Those who choose to have a dog must recognize the duty they undertake to provide food, shelter, training, exercise, and medical care for the animal. That said, most Muslims recognize that pets are not our "children," nor are they humans. One should keep things in perspective.

http://islam.about.com/od/islamsays/a/Dogs-In-Islam.htm

Dogs are not like cats, they can't wander around the house according to Islam and if you have enough room in your home for the dog to have his own space, then it's okay I guess.