So first contact your partner/ Nintex account to get information on how to access your Nintex Workflow Cloud application.
Once you have an access, you could follow these steps: Stronger Together - Nintex Workflow Cloud & Office 365 so that you will create a scheduler for your Nintex for Office 365 workflow, however if this is your first workflow then this approach may be to difficult.
On the other hand you could try to just create a Site Workflow, that queries a list where you have your items with "Reminder Date", then for each one having the date equal to current date does what you described above, then after it processes all items from the collection it simply pauses itself for a day. The next day it starts from the beginning.
But I would recommend the following solution in Nintex Workflow Cloud:

Before you begin:
- Get GUID of your List, where you have the Items. To do that, simply go into List Settings and get the guid from the URL, removing the %7B and %7D characters:

- Now open the URL: https://your-tenant.sharepoint.com/site-where-the-list-is/_api/web and look for the element
<d:Id m:type="Edm.Guid">
Then, copy paste its value - this is the Web GUID. - You will then use this values as variables.
Now go to the NWC, and create a workflow:
- Create two string variables:
- ListGUID - paste the obtained guid as default value;
- WebGUID - paste the obtained guid as default value;
- Set Start Event to scheduled:

- Then add action from the SharePoint Online group --> Query List, and configure it accordingly:
- Create a connection to your tenant
- Point to the site, where your list is
- Pick the list
- Set the Condition: Reminder Date is on Current Date:

- Store item IDs into the Collection variable:

- Now "Loop for each" action, through the Collection of returned IDs.
- Store item into the Integer variable.
- Now "Retrieve an item"
- Again, configure it to point to your list with the Reminder Date and the person or group column holding data of the person to whom the task should be assigned - NWC stores it as an Integer variable:

- Now "Create item" - point to your Tasks List and create a task for the selected person. In "related items" set this JSON:
[{"ItemId":MatchingItemID,"WebId":"WebGUID","ListId":"ListGUID"}]
Save and run - you will have a scheduled workflow creating you tasks.
Now I suggest to create a Nintex for Office 365 workflow on the Tasks list, that is triggered once a task is modified - so assuming the assignee approves or rejects.
Once approves, get the related item of the task, update it setting its "Reminder Date" + 12 months.
And I guess it does the trick! 
Regards,
Tomasz