Hi and welcome
I do understand where you are coming from and why you are thinking about it - however what you are saying so far (though I appreciate that you may only have posted a small amount of your feelings and motivations) doesn't fit with the reality of adoption today.
Adopting a second child, absolutely is something many families do. What social workers are looking for (and what waiting children need), are parents who are primarily coming to adoption because they really want a second child themselves. Hoping that your BC and a new child would become very close is something everyone hopes - but 'giving a BC a sibling' can't be the primary motivation for adopting. So it depends on how much your desire for a second child is about you and DP, and how much it's about your DD? If it's mostly about your DD, adoption is unlikely to be for you, IMHO. If it's firstly about you and your desires for two children, it might be an option for you to explore further by doing more research on adoption today and the children who are waiting for adoption.
This is because most waiting children have some form of additional needs (especially emotional needs), and it's important that everyone goes in expecting to be dealing with family life being probably different from how they initially imagined. And obviously there's no guaruntee that two children will be close - they might well become very close, but obviously SW's need to be sure the family won't be regretting the adoption if a year down the line, BC and AC have a personality clash and don't get on well at all, or AC has additional needs which are impacting quite negatively on BC (or vice versa).
In terms of age gap, you usually can't adopt any child older than your BC because it will be considered too high risk, to my knowledge it very rarely happens except in adoptions by relatives or foster carers. Any AC would, for nearly all agencies, need to be at least 2 years, but many will advise that 3 years+ is better. It's individual and personality based to some degree, and some people find a 2-3 year age gap has been fine for them, others have found that a larger gap is very beneficial because of reduced competition and jealousy, not sharing friends so much, basically having their own space in a way. Again it's largely because new child has emotional needs which are intense in early days but may continue to be intense for a long time (or forever). SW's for instance, generally like the idea of your BC having started primary school, or being in nursery because it gives you some hours in the day to really focus on meeting your new childs needs. They like the idea of you being able to explain things to your BC and have them understand a little. That doesn't mean that people with 3 year olds don't adopt 0-1 year old babies, it can certainly happen (when I say baby, I mean about 8/9 months and upwards, babies under ~7 months are not frequently waiting to be adopted).
I have to say, in terms of age gap, there's a 19 year one between my first DC and my last - and they are very close, they adore the bones of each other. DC2 and DC3 are birth siblings with a significantly smaller age gap, yet they aren't as close and their relationship is very complicated. From my experience, closeness is a lot about individual personalities. I hope people find that reassuring! In the end, two extra years age gap is unlikely to mean the kids aren't as close.
I'm out of date enough with the adoption process that I'm not sure about referees (my mum was visited but she lives close to me) - only way is to ask the agencies individually, they will have different policies.