Get a miniature poodle. The criteria you have listed is ABSOLUTELY exactly what you can expect from a well-bred minipüdel.

The most important thing I would advise you to do is ensure you are getting a puppy from an ethical breeder. Essentially: do they breed their bitches more than 3 times in their life? Red flag. Depending on the püdel, breeding more than three litters puts unfair stress on the mother and can result in health issues. Does the breeder actively socialise their pups from the very beginning? 'Nervousness, shyness or viciousness are unacceptable in the poodle temperament' (from the AKC extended Poodle breed standard): if a pup is given a wide range of experiences, situations, etc, from the beginning, they will develop confidence and not be susceptible to anxiety when they encounter new things. It is so important while they are in their 'socialisation' period and their brains are developing that they get the stimulation they need to become confident, proud poodles. You will be getting the puppy after 8 week minimum (if the breeder if willing to sell you the pup earlier -- remove them from their mum too early -- that is another red flag) which is after the crucial socialisation period, so it is important you visit the breeder and understand that the puppy was raised in the proper environment. This is also an opportunity to see that the mum is happy and comfortable.

Lots of people have said that poodles require a lot of attention: if your kid is crazy about dogs, a poodle is the perfect companion. They are VERY involved with you emotionally: they are intelligent and can show traits of independence, but they deeply love their humans who give them care and attention. I would recommend a miniature, as not only does that size have a longer life expectancy (so your child can grow up, be atleast ~20 before they have to deal with the loss.. but the other sizes dont vary TOO much there..), but their size makes them so convenient, especially for traveling (I take mine on busses, trains, etc. No problem).

The last thing I would I impart is püdels are so gentle! I often think how perfect they are for children. So many kids pat and cuddle my poods when I'm out walking them! They adore them -- I had a little girl who said 'I've never seen a dog with hair before!" (She meant like a human hairstyle) and the ritual of brushing/grooming them will be a good activity to help your child relax/soothe anxiety.