Well I have adopted four children, I have seen that you have been trying to conceive, this can delay your suitability, not stop it. Generally most adoption agencies require at least a years wait after you have stopped
TTC before you will be fully approved, but this depends on what you want, if you wish to adopt an older child (normally 6+) they are more likely to relax this rule. Any adopted children are supposed to be at least two years younger than any other children in the house, but they often relax this to 18 months.
No one within the household can have any past offenses against someone under 18 and no one in the family must have committed any crime in the past two years.
Your social worker has to meet every member of your immediate family, which for us meant my brother traveling all the way from Italy, then my partners mother hates him, so that was interesting to say the least. Then they need to know about every past relationship, why it ended etc and they may also need to talk to ex partners, they are pretty much guaranteed to talk to an ex wife/husband or the parent of any of your children if you are no longer together.
You need referrees as well, one can be a family member, the other a friend/colleague, but you must have known them for at two years.
You have to have a full medical, so if you or your partner have a condition that can shorten your life significantly, then you would not be approved, as you have to be healthy enough to care for the child/ren until they are 20. So, certain disabilities could also rule you out.
They are the most important things in approval, however 94% of people are approved, it shouldn't take more than 8 months to get your final decision.