Hannah Burgess, 27, recently shared an online video in which a driver initially declined to transport her golden retriever, Morris, before eventually relenting.
The proposed hike, intended to cover mounting compliance and administration costs, will be decided by the council's regulatory committee on Wednesday, June 11.
A taxi driver was reportedly assaulted in the quiet Essex village of Mistley in the early hours of Sunday, June 8, after a passenger fled his vehicle without paying.
The decision was made at a taxi licensing meeting in May, scrapping the £29.90 test component for hackney carriage and private hire licence applicants.
The last tariff increase in Exeter was in 2022 and a consultation is taking place and members of the public can make comments right up until 13 July.
Drivers report struggling to earn the minimum wage, with some operating for full shifts and taking home as little as £20 after expenses.
The decision comes after mounting concerns within the taxi community regarding abuse directed at drivers, alongside demands from passengers for increased reassurance during their journeys.
The initiative comes in response to growing public concerns that passengers are being left stranded if they don't have physical money, expecting to pay with modern options such as contactless cards or smartphone apps.
Three taxi drivers in Huntingdonshire have had their licences revoked in recent months, with more than 20 vehicle licences also suspended.