I assume you're referring to the PT-61 form as opposed to the quitclaim deed itself. If so, yes: the property tax parcel is the same as the tax map number and, in Georgia, usually looks something like this: 052-4A-000-068.
There is no technical need to place a tax map number on a deed, quitclaim or otherwise. A legal description of the property is, however, required.
I feel compelled to caution you about using office supply store forms. I have seen invalid deeds in deed records as a result, which can lead to quite a mess.
No attorney-client relationship or privilege is formed by this communication.
Totally agree re: office supply form = potential for unintended consequences. For the record, if I was preparing a deed I wouldn't need to put the tax parcel on the deed itself but as previously noted you will need that info for the transfer form for GA. Other Q's: What are you trying to do? For example, if you are deeding yourself off title (e.g. to your wife) you may cut off your protection through title insurance, etc. You may create issues for heirs, etc. Is the form proper for GA? Will you end up having to "re-do" this deed later? There are many little issues that could pop up from using a 'form'--yes, I'm being a bit protectionist but you are talking about a house, which is typically a sizeable investment vs. about a $50-100 charge from an actual attorney to prep a proper instrument to file. Find a local attorney and feel free to shop around!
Just plain over-the-counter commentary, no lawyer-client relationship created. Seek your own counsel for true 'legal' advice. This is just an off-the-cuff response to a short question on the web; not to be construed as legal advice.