You can't adopt a child the same age as your daughter. SS will insist on at least a 2 year age gap. This is to protect your child, and the placed child. An adopted child is not a 'playmate' for a birth child, and will probably need parenting differently too.
My children are my own so I love them like my own. Sometimes I think I love them more than I would have loved birth children, because it was so hard to become a family.
Most children in UK available for adoption have come through care proceedings, rather than being relinquished. So there isn't really the option for the 'parents to want them back', though prior to final adoption order they do have various rights to try this. Children aren't generally placed for adoption unless it is really clear that the birth parents cannot parent adequately. There are relinquished babies of course, but not as many as 40 years ago.
If you 'foster to adopt' then this can be better for the child, but you would have to be prepared that the child may be returned to birth parents if they get their act together. foster to adopt could have massive impact on your birth child as she could form a bond, only for the child to be returned. I don't known whether they would even let a couple with a birth child foster to adopt.
Normally when a child is placed for adoption it then takes ~6 months before the final legal adoption. More for an older child (15 months for us).
Once they have agreed to take you on, you have an indepth homestudy which takes ?6 months or so. Then an indeterminate amount of time for matching, as they find the best parents for the child, not how long you have been waiting for.
You are very young to be adopting. It shouldn't be a barrier, but SS will find it unusual, and unusual often means harder to be accepted. They may well wonder whether you have the maturity / experience of life to parent a traumatised child, and cope with their past history etc.
One of you should be expecting to be off work for at least a year. Does that fit with 'buying a business'?
The dog may be an issue, a pet assessment would be needed.
You can be assessed by your Local Authority, or a neighbouring one. Or a voluntary agency. VAs don't have their own children to place, and are often used for 'harder to place' children.
hope this helps