Hi Becca, welcome to Permies! One way to make more than $1K from your farm is to look into the USDA's Conservation Stewardship Program. Here's a post about it:
Getting Paid to Homestead
If you need the $1K to be actual income from farm work, you can do it a number of ways. Some of it depends on your local market. What's the going price for organic eggs in your area? The math scales up pretty easy to see how many chickens you'd need to make that much in eggs. Same for honey. I'd imagine that earning hundreds of dollars from chicks would be harder. Unless you know something about breeding chickens it may be hard to sell your chicks. I'm sure this is highly market dependent.
You could make
compost and sell it.
Starting a nursery would be awesome. Once you have a row of raspberries, it's easy to harvest 20-80 baby raspberries a year to pot up and sell for $4 ea. Learn how to do cutting propagation and get some good permaculture or niche plants started as parent stock and you're off to the races. I'm starting hardy kiwi, highbush cranberries and aronia from cuttings this spring. So far it's working out. I have 5 little 6" pots with 6-8 cuttings in each. The aronia (15 of the cuttings) would fetch $10-15 as bare root saplings so I'm saving $150-225 by starting them myself for my food forest. All that in a 3 square foot area.
Good luck!