Nobody is being 'dramatic'
Sorry but some posters definitely are being dramatic. Telling OP to "complain to Ofsted!", go to the Govenors!" "demand to see their risk assessment!", "threaten to remove your child!"
How about calling the school up and having a calm conversation with someone about her concerns in the first instance?
I am NOT a dog person. I don't own dogs, I don't care about dogs, I don't particularly enjoy being around other people's dogs. But I don't understand why people jump straight to outrage, without knowing the full facts.
Firstly, as a parent you have no right to see a schools risk assessment, unless that risk assessment is about your individual child. But you can ask questions, enquire about how they manage allergies, children who are scared of dogs etc. I would suggest OP do this before making a "complaint" based on assumptions.
I've worked in a lot of schools and I've never known a child be forced, or even expected, to interact with a school dog or even be in close proximity to them. If this happened you would have every right to complain. But if simply being on the same playground as a well-behaved dog, who is on a lead and not behaving in a boisterous or aggressive manner, is enough to distress you or your child then I would say that's a severe phobia that needs to be addressed through some sort of therapy. Also, if this was the case presumably you could make your child's teacher aware, they would speak to the HT and the dog could be kept at a distance from them.
I'm also surprised some people are accusing the HT of hypocrisy for not allowing parents to bring their dogs onto the playground at drop off/pick up. Can people really not see the difference between ONE dog, that is known to staff and under the control of the HT, and dozens of random dogs turning up at the same time every day? Some parents may not be responsible dog owners, some dogs are aggressive and fight with other dogs, people don't clean up after their dogs or train them properly. I'd be really surprised if any school allowed this.
I'm sorry OP but I had to laugh at your comment about the dog not being a "professional"! Dogs don't need professional qualifications to be a 'school dog'. They do need to have a calm temperament and be well trained.There is specific training that you can access for school dogs, reading dogs and therapy dogs, but how do you know your HT hasn't accessed this? Do you have reason to believe the dog is not not calm and well-trained?