I have a Self Employed account and I'm trying to Invite my accountant. There is no Accountant heading in Settings.

Welcome to the Community, thalia1. I did some research into this topic and would be more than happy to share my findings.
 

According to Intuit's article about inviting an accountant, this feature is still available for subscribers. At the same time, I see what you're saying here and wanted to test it out myself. I accessed our QuickBooks Self-Employed test drive account, and repeated the same steps you followed.
 

Here's my results:

As can be seen, I encountered the same problem you did. The option isn't displaying, while the support resource says it's there.
 

The next thing I decided to check was our ongoing/solved investigations, to see if there's any records about this issue. Currently, there isn't an investigation about the Accountant option not displaying when selecting your Gear (⚙) icon.
 

With all of this being said, what I'd recommend at this point is contacting our Customer Care Team to further research why this is occurring. They'll be able to pull up your account in a secure environment and create a ticket for Intuit's Product Investigation Team to look into further, if necessary.
 

Here's how you can get in touch with them:
1. Use your Help (?) option.2. Choose Contact us.
3. In the Ask a question (or tell us what's wrong) field, explain what you're reaching out about.4. Click Continue.
5. You'll be given three different options for contacting support. Make sure to select Start a Chat or Talk to a specialist.
 
Definitely be sure to review our support hours for when representatives will be available.

I've also included an article which explains more about contacting Intuit: Contact QuickBooks Self-Employed Support
 

If there's any additional questions, I'll be here to help. Have a great day!

Has this been solved or figured out? I have a client that would like to do the same. I’m afraid they may have to purchase a basic or plus account… Not sure they want to and, while I can coordinate money 6 months of records from one to the other, I’d rather not if I don’t have to (work smarter, not harder).

Let's find out why your client is unable to invite an accountant, ParrysBookkeeping.

Generally, you'll be able to see the Accountant option when you're logged in to your QuickBooks Self-Employed (QBSE) account using a web browser. If the option is unavailable, your client may be using another version of QuickBooks product. 

If they are using QuickBooks Online (QBO) account, let them select the Manage Users option so they can access the Accountant option. This ensures they'll be able to add their accountant. To give you the detailed steps of the process. I've provided the steps for them to follow:

1. Sign in to QuickBooks Online as a primary admin.
2. Select Settings ⚙, then select Manage users.
   
3. Select the Accountants or Accounting firms tab.
4. Enter your accountant’s email address, then select Invite
   

However, if you're using QuickBooks Desktop, let your client set up an External Accountant for them to access the company file without a need to sign in as Admin. Usually, An External Accountant user has access to all areas of QuickBooks, except customer credit card numbers.

Furthermore, learn how to access accountant-specific tools to enhance your bookkeeping. These make reviewing your QuickBooks client's accounts more efficient. I've added these resources for your guide:
 

• Use Accountant Tools And Features In QuickBooks Online Accountant
• Accountant Tools In QuickBooks Desktop

Let me know if you have any concerns when inviting or adding an accountant. I'd be glad to help. 

Is there no solution to this?  I am seeing this right now with a client

Hi sshaw1857900,

The option to connect with your accountant isn't available in QuickBooks Self-Employed in Canada.  However, you do have the ability to share reports and other tax information with your accountant or bookkeeper, by exporting the relevant reports and then send them via email.  

You may want to consider an upgrade to QuickBooks Online EasyStart, Essentials, or Plus.  These products allow up to 2 accountant users per subscription so you can easily invite them to work directly in your QuickBooks account.  If you should decide to make the switch, there are two options when it comes to moving from QuickBooks Self-Employed to QuickBooks Online.  Here's how to Switch from QuickBooks Self-Employed to QuickBooks Online.

If you would like to see this available in future updates, I encourage you to submit feedback.  Navigate to the Assistant feature, then type and enter "Feedback". Follow the prompts to share your suggestions. 

Feel free to reach out again, if you have other questions.  We would be happy to help!