Right now we are in the middle of chol hamoed Sukkot – the intermediate days of the festival. On these days we are still prohibited from performing many of the same acts of Melacha that are prohibited on Shabbat and Yom Tov. The exceptions are acts which are necessary for the holiday itself (cooking), financial loss (going to work), etc. Other acts are specifically prohibited during chol hamoed in order to prevent people from holding off on performing them before the holiday just so that they can do them during chol hamoed. The idea is that right now we should still have a festival atmosphere.
Among this last group is getting haircuts, shaving and doing laundry. Yes, it is forbidden to do laundry during chol hamoed. There are some exceptions to this rule (speak to your posek for details). I thought that I had remembered that one of these exceptions is washing clothing for a child. To check this out, I looked it up in my trusty sefer Chol haMoed k’Hilchata. One of the good things about this book (and others like it that tend to give as many strict rulings as possible) is that when it says that something is permitted, it is pretty trustworthy.
In the section on washing baby’s clothing, the following is written (chapter 5:15)
Clothing for infants and very small children, since their way is to make their clothing soiled with Great Frequency (??????? ?????), and all the more so the diapers in which they do their business, on Chol haMoed it is permissible to wash the amount of clothing that they require at the moment (Rema 534:1)…because they need many clothing, all the time (ibid)…it is impossible to set a limit [for the amount of clothing that they may need at any one time]
Oh how well I know.
(In a different footnote it says that in a washing machine, as long as you are running a load for your infant, you can put in as many clothes for then infant that will fit in the wash. However, you cannot include your own clothes in the infants wash – footnote 53)