Same Sex Adoption

Although same sex adoption has come a long way and is recognized now in some countries (14 at the time of this post being made), unfortunately it is still not completely recognized under Australian law and some other countries. Couples of the same sex aren't even able to marry in Australia currently, but are instead recognized as a de facto couple when cohabitating together.
Adoption in Australia for any couple, whether they are heterosexual or gay is really difficult, as it stands in the year 2012. It's becoming harder and harder with the number of actual adopted children dropping dramatically.
Same sex adoption is sometimes referred to as LGBT adoption which stands for adoption of children by Lesbian, Gay, Bisexual and Transgender (LGBT) persons.
While the wheels seem to be turning slowly, there are more medical, psychological and social welfare communites who are of the opinion that children raised by gay and lesbian parents are just as likely to raised well-adjusted children, as much as heterosexual parents.
Of course there is still alot of debate out there about this subject and not everyone is in agreement with this.

Here's a short video which tells of some of the current obstacles same sex couples deal with when trying to adopt:

Countries that currently allow same-sex couples to adopt (current at the time of publication in 2011) are:

Andorra, Belgium, Canada, Denmark, Iceland, the Netherlands, Norway, Sweden, South Africa, Spain, the United Kingdom and Uruguay.
It is also legal in 14 states in the United States, the territory of Guam, and one territory and state in Australia (ACT and WA).
In Germany, Finland, Greenland, Israel, and the Australian state of Tasmania, "stepchild-adoption" is permitted, so that the partner in a civil union can adopt the natural (or sometimes even adopted) child of his or her partner.
Laws are changing all the time, and at the end of the day it is the law that the decision to adopt to anyone is governed by.
If you do have an interest in adoption, it might be a good idea to start with the countries that do allow adoption, and seek some advice from adoption agencies in those places first.
Perhaps you may find some kind of answer.
Adoption is difficult and something not to be entered into lightly by anyone. It's often a drawn out process that can take alot of time, paperwork and emotional energy before you even see your baby.
The adoption process often involves alot of money, along with travelling to the country you adopt your child from.