Is it permissible for a person with epilepsy to own a dog to draw off electrical brain activity and alert her to seizure times?

We ask Allah to heal and cure you. The general rule is the prohibition of owning a dog, except for what the Shari'ah has permitted. A group of scholars have permitted owning a dog for a beneficial purpose, by analogy with what is stated in the texts. This is based on the statement of Al-Nawawi: "The preponderant opinion is its permissibility by analogy with the three [exceptions], acting upon the understood reason (illah) from the hadith, which is necessity," and the statement of Ibn Abd al-Barr: "And in the meaning of this hadith, in my opinion, enters the permissibility of owning dogs for all benefits and for repelling harms, if a person needs that."

Therefore, there is no objection for you to own a dog for the mentioned purpose, while taking precautions regarding the impurity of its saliva as much as possible.