You lent your brother and his wife $7,000 last year for their house purchase and they paid it back. So why do you only have $4,500 in savings, when you should have that $7,000? OK, you are not giving us the whole financial picture, that's fine, but of what you have said I'm not sure I understand.
If your brother could save $7,000 in the first year after buying a house and pay it back to you that does suggest to me 1) he was responsible in how much house he bought and didn't overcommit himself (ie he was short of capital because the mortgage amount was less than he expected, but has sufficient income to cover his expenses with enough to spare) and 2) he took the obligation to pay you back seriously. I like this brother of yours (fond of my own brother too). So while your brother is temporarily out of available capital but has proven himself responsible with money. I understand (never done it myself) that adoption is a tricky and expensive process, but that for a childless couple to bring a child into their lives can be a wonderful thing for both them and the child. Your brother hasn't had time to build up enough capital yet after the purchase of the house and paying you back in the last year, also understandable. So I'm sympathetic. Helping this adoption would help to bring a new niece or nephew into your life, which could be life enhancing for you and the rest of the wider family too, so there is a potential direct personal benefit for you as well (or not, of course, if you have personal feelings against adoption and kids). Those are the things which can speak in favour of the loan.
Now, reasons against the loan.
1) You need to put your own lifebelt on first. This is one of the things which seems to be concerning you: you don't have much spare cash at the moment for whatever reason, and you may have need of this couple of thousand or so for yourself before it can be paid back. All you can do on this one is take a reasonable look forwards over the expected payback period and list the reasons you might need the money. If it looks reasonably likely that you will need it yourself for expected expenses (eg moving and need a deposit, school fees to pay) or you need a safety amount on principle (car might crap out and need expensive repair or replacement) then you have to say to your brother "sorry, I'd love to help, but I've only got enough to cover X which is coming up: it's bad timing for me and otherwise I'd have loved to help".
2) Your brother can't afford it. Adoption is expensive, children are expensive. There is the capital expense of adoption, and the running costs of a child in the house. If the running costs of the child are within budget I would be less concerned about helping out with the capital costs. You already have evidence from the previous loan payback that your brother seems to have at least $7,000 to spare in his annual budget. That's not bad in the first year of house ownership, but whether it's "covers the first year of an adopted child in the house" money I don't know, and I don't suppose you do either. I think you need a financial plan from him before you go ahead with any loan.
3) Whatever you decide, you need to make your brother aware that your own financial circumstances are circumscribed (eg you've been paying off debt, you are looking to move jobs, you want to save for a house) and that interest-free loans to him cannot be a habit because you want to get to the position he is already in and have your own home.