Agencies like one of you to be able to take 12 months off, BUT not always and it may depend on the child's age you adopt.
We bought our son (7 months at the time) home in April (couple of years ago) and our adoption order was granted in October, so anything after that was our decision and nothing to do with social services (so 6 months after bringing our son home). But we did say we could take the time off.
Rented house no problem, but they would need you to have a room just for the adopted child, whether your partners child only stays at weekends or not. The adopted child/baby would need a room of its own.
Also they like the adopted child to be at least 2 years younger than the bio child.
Check both your companies adoption leave as it may be financially better for your partner to have the time off rather than you. I'm self-employed so got nothing when it came to adoption pay, but my husbands company had a policy that ended up being really good (after a battle to get his national healthcare company to put their adoption policy in line with the maternity one!). He ended up getting 3 months at full pay and 6 months at half pay, and then statutory for the last 3 months.
They will look into your medical history, you will have to have a medical with your doctor, which is then sent to the agency's doctor to review.
You haven't said what your medication is for, and you don't have to, but be aware this may be looked at in more depth.
If you have still been trying to conceive in the last year it may be worth thinking about if adoption is now your only avenue to have a child. Agencies will want you to not be considering any other options (natural, IVF etc) if they are going to progress with you.
Your finances will be looked at, what comes in and what goes out, so they can see you can 'afford' a child.
Your family history will be looked at, what relationship you have/had with your parents and siblings, and depending on the age of your partners daughter she may also be spoken to.
How long have you been with your partner? Your relationship will be looked at too, along with your education and work history.
We had a lovely social worker, I still send him photos every few months of our son, but this can differ massively. Ours used common sense, was very experienced and knowledgeable, and this really helped us. Some others I have heard about are more about ticking boxes, aren't as friendly and can be inexperienced.
Hopefully the above hasn't scared you, we adopted nearly 3 years ago but it is very intrusive, frustrating and there is a lot of paperwork. The whole process for us (with an experienced social worker) took about 9 months, before we got approved. Then you have to wait to be matched with a child, and we were very lucky to be matched 1 month after being approved, but some people take months/years.
But we now have a 3 year old who is amazing, and it was all worth it!