prob not egg stage, they have to walk thru it, like DE.
water wont take much into solution, would only make in 4L batches at a time or less. make sure to use just a little soap in there. say 1 tbl. to a Liter.
Danger is in breathing powder in. Make sure you are getting pure Boric acid powder, not mixed with other toxics. Can find at folks for biodiesel, but you need the finest powder you can get, so i usually look for roach powder.
Spray it up onto the bottom of things they could be hiding in, and on vertical surfaces that wont hold the dust.
Dust works best along edges of rooms. put down a bit, and sweep it along baseboards, etc. Bugs will usually get to an edge, and follow it.
Don't leave free dust or piles around, if the kid is sniffing the floor.
If you are the carrier, try mixing a little cinnamon oil into your
shampoo and body soaps too. will keep em off you, but some folks are sensitive. test first.
I would dust my hair one eve for a couple hours, (just enough to keep the skin dusted, you dont need to be a ghost), and wash it out before bed too.