A more common and natural way of communicating this idea would be to say: :"Will you buy some more food? We having nothing to eat." -or- "Will you buy us some food? The fridge is empty."
In your expression, "There are nothing...." should be re-written as "There is nothing...." Also, it is technically more accurate to ask someone if they "will" or "would" do something rather than if they "can" or 'could' do something. When you use "can", you are asking them if the are 'able' to do something when, in this context, you are actually asking them if they 'will' do something. However, I would not worry about this last point too much since most native English speakers are not aware of the difference.