There are masses of after-school activities BUT they are in French and a minority in Dutch in Brussels. There are English after-school activities too, but if English is the home language, why would you do English after-school too and not French or Dutch here, it would seem pretty pointless to come here and just remain in an expat English bubble. Then if you go for after-school clubs in French or Dutch, unless your daughter already speaks these languages or you are fluent in them and plan to school her in these languages, she might find it frustrating socially and also she might find it difficult being unable to follow what is going on.
I can understand you wanting to home school, as you're only here for a year, but I can also see your daughter might be exceptionally isolated as you simply won't find anything day time with other children, other than seeing school groups visiting museums, swimming etc.
If you chose your school wisely and your daughter is confident in herself, a year in a French or Dutch or a private French-English school could be quite a positive experience. Our daughter is friends with a Japanese family who brought their children aged 6 and 8 years old at the time they came, they stayed only a year as their dad was a visiting lecturer, they did so well in coming out pretty fluent in just that time. Japanese parents do seem to have a very "throw them in at the deep end and they WILL swim" attitude, all the Japanese parents at our children's French school are great at leaving their children, turning around and walking away, no fussing, no reacting to any crying, their children seem to settle far faster than the children of other nationalities. None of the Japanese children, except for the half Belgian ones, stay more than 2 years, but their children all seem to adjust fast to a far more alien culture and way of learning than they would have in Japan.
If you are a teacher yourself and English is your home language, why not consider doing after-school English, offering it to others at the same time? There is literally one person only in Brussels who advertises after-school English as a group to native level English speakers, you could set up an ASBL and teach English to native speakers after school and fill classes quickly, especially 6 to 12 year olds, as there are so many English speakers in French and Dutch schools who only get to do English from aged 14 years old, then it's only 2nd language and not aimed at native level. Your daughter could then go into a French, Dutch or French-English private school (would cost you 6k) for a year.
You might want to take a look at this school to the east of Brussels, in Kortenberg. I'm sure you'd be familiar with Summerhill school in England. The "teaching" language is Dutch, at a guess there are perhaps only 10 children there, the children would have to vote on whether they'd even accept your daughter as a student! It's not Brussels, but a good location if work is on the east side of Brussels like Vilvoorde or Zaventem. I'd live out near the school, if I had a child there, as Brussels is 90% French and Dutch speakers have a hard time here.