Some roundworms are zoonotic, so you could get them from cats easily enough. But it usually has to do with cats getting into sand pits & even though you pick up the poo, the eggs stay in the sand undetected until a child gets to them.

But most worms kids get are threadworms/pinworms. I use a wormer which is for 12 months and up, and because Jovie is over 12 months I didn't worry about breastfeeding her while taking the worming. She was the one with worms anyway, so needed it. I had to redo them at 4 weeks because of the level of infestation on Jovie. At the same time I washed all bedding & clothes in hot water & hung in the sun to get rid of worm eggs & now 6 weeks on it looks like I didn't do a good enough job because Jovie has worms again .

I actually took a worm to work to find out which sort we had, and it was a threadworm.