Tecnically, Jewish Law does not regulate the length of time one must wait before donating the clothes of a deceased person. However, during the period of the shiva, usually lasting for 7 days after the person has died, mourners refrain from conducting all business. So it would be appropriate to hold off on the practical affairs of the household until after this first period of mourning.
Let me also say that if this question was submitted by someone who has recently lost a family member, I wish you comfort among the mourners of Zion and Jerusalem.
During the yizkor service, when we memorialize our loved ones, we ask God to remember them, and we pledge to give tzedakah on their behalf. After someone dies, a common Jewish prayer is that his or her memory should live on, "as a blessing." I believe that both of these concepts can shed light on your question.
Judaism values acts of tzedakah, monetary and otherwise, and understands that even though a person no longer walks this earth, their values as well as their possessions still have the potential to make a difference in this world. With that in mind, I would suggest that the family take some time to consider an appropriate place to donate the clothing and then do so as soon as possible after the period of shiva has concluded. I would also suggest that the clothing be specifically donated in his or her memory. Waiting until the shiva period is over allows you to take time to mourn and remember your loved one. And then, as you begin to walk back into your daily life without him or her, this donation would be something tangible to ensure that their memory and presence will continue to be found in this world.
There is also a strand of the tradition that talks about acts of tzedakah serving as "atonement" for the deceased. You may or may not believe that your acts are causing God to forgive your loved one for any misdeeds in the world to come, but the notion that your actions are connected to your loved one's existence beyond this world is powerful as well.
This is an important question that often arises when someone in the family passes away. Jewish law (halachah) offers no specific guidelines for whether or not you should donate the clothing of someone who dies. Furthermore, there is no halachic precedent that dictates when you should donate such clothing. This being said, one does not do work during shiva, the initial week of mourning for a parent, spouse, or child; so the effort to collect and distribute during this time period the clothing would go against such a precept.
The desire and timing of when to donate the clothing would really be an individual decision. It is an emotionally charged process that can be difficult, though the outcome is certainly a great mitzvah (clothing the naked, malbish arumim).