It's possible to remove your own appendix too, but neither that nor do it self adoptions are a good choice. I say that not to be flippant, but to reinforce just how bad an idea it is to try.
No area of law is more dependent on perfection in detailed paperwork and technical procedures than adoption, and even the simplest case would generally be beyond the abilities of a pro se litigant. With something as important as a child, it would be a horrible risk to take.
Probably only about 1% of attorneys have the knowledge and skill to do an adoption properly and you want to retain someone who has significant adoption experience. Oftimes the cost is a lot less than you would think. I'd have to know more about your case to give you estimates on that.
I've done adoptions for 29 years, and even with that experience level, it takes effort to keep up with the law in this field.
I would not recommend it. However, if you have time to research and understand the law, obtain forms used in the court, and understand the adoption process, you can do it.
It is possible to file your own adoption, though you may have more success with an attorney assisting you. There are several difficulties with filing your own adoption:
1. There are several different types of adoption, and each requires its own paperwork, though there is some overlap. If you miss something, your adoption may not be granted, which could result in you having to refile and incur additional costs.
2. While the Georgia statutes on adoption are helpful and pretty clear, there are adoption issues that are not addressed in Georgia's laws, in particular the requirements of several federal laws. A person handling his own adoption could unwittingly violate a provision of one of these laws.
3. It may be easier to deal with court administration by having an experienced lawyer advocate on your behalf.
At the very least, you may wish to hire a lawyer to review your paperwork and identify any deficiencies before filing. Depending on the type of adoption, another alternative may be for an attorney to assist you with preparing your adoption paperwork to file with the court but not to represent you in court.
As has been suggested, you may want to "interview" several lawyers about handling your adoption. The affordability of the fee may surprise you, and you may find a lawyer that is a good fit for your case. Be aware that some attorneys do offer consultations at no fee, but others charge a consultation fee.