a crate is like a kennel or a cage where to dog can sleep at night or if you go out for a couple of hours. keeps the dog safe if they are chewers (you don't want them munching on a cable) some people split the crate into a section to sleep and a section to toilet, i don't like this as it is conflicting information. dogs in general don't like to toilet where they sleep. you will find if you dog is ill and couldn't hold their toilet or was sick over night they will bunch it up in the bedding and push it to the side. sometime spending the night in the corner as they don't want to be near the dirty side.
what you are thinking of for cats may be a cat litter tray, you do get a version of this for dogs with fake grass.
as for size, you want one that will be big enough for an adult cockapoo to stand up and turn around. so you will need to find out how big mum and dad are, Sunday may be a little bigger or a little smaller than them.
this is my girls crate, it is massive because all three share it ours can fit a doberman (the dog owned by the person we got it off) lol it doesnt always look like this, the photo was taken at christmas and i was feeling festive lol
a 24inch crate will probably do. or ask the breeder if they use a rate and what size they use.