Hopefully, someone with experience doing so, will contribute their answer.
I'd suggest you try to present it from a business value standpoint, meaning what the organization will gain by doing so (more access to highly qualified talent, engagement inc. productivity/attendance and longer retention of the talent (which results in lowered costs of recruiting, on-boarding, retraining and reduces intellectual capital loss). Also, potential decreased health care costs due to reduced stress in workplace. Basically, this should be a presented as benefit with significant value.
It will strengthen your proposal to have some figures supporting these financial wins for the company and also present what will be done to satisfy the concerns of those who may not share the same mindset (such as what can be done to alleviate environment for those with asthma or allergies with separate areas and consideration to the maintenance required). If there are non-dog owners, who you can make your allies to support this, especially anyone in HR or management, that will reduce barriers towards implementation.
Here are a couple links that might help as you brainstorm this further:
https://www.shrm.org/resourcesandtool... http://www.slideshare.net/TowersWatso...