What you can do is further dilute the penicillin with some lactated ringer solution so that it will be easier to measure. You can get test tubes with a rubber top for mixing injectable medication. You draw up some penicillin (1 cc for example) and put that in the test tube. Then you draw up some of the lactated ringer solution (1 or 2 cc's) and put that in the test tube.
Then depending on how much you diluted the penicillin, you just draw more of it into the syringe for injection. If you did a 1 to 1 ratio, then you would double the amount. If you did a 1:2 ratio then you would quadruple the amount.
If the dosage is 1/10th of a cc for 5lb, that would be 0.1cc per 5 pounds, which would be 0.02 per 1 pound of rabbit.
You can go to a people pharmacy and see if they have some small syringes for injecting insulin. I have some syringes from the vet that measure by 0.1cc's. So if you diluted the penicillin enough, you could use that to give the injections.
Make sure to mix, by rolling the test tube, very well before injecting. The penicillin will separate from the lactated ringer when it sits for a bit. The reason you want to roll the container is to minimize air bubbles in the solution.
If you can get me the concentration of the penicillin and the weight of the baby, I can calculate the proper dosing as recommended by Medirabbit for you.
http://www.medirabbit.com/Safe_medication/Antibiotics/Safe_antibiotics.htm
And I'm not sure why my vet likes chloropalm for young rabbits. He's done lots of work with rescues so I think he has had lots of cases of having to treat young rabbits, and most people aren't comfortable giving injections, so he had to find the best oral antibiotic.
Hope that helps you!
-Dawn