Antibiotics are (as far as I know) always injected best into the muscle, so I just get mine onto the milking stand and wack the syringe into their upper hindleg towards the bum, just where it is quite fleshy. As they are usually having a wee treat at the same time it is all over quickly...
I would check with the vet about the dosage though, you will need to have some idea of her weight. Not sure if goats get the same as sheep, but I think they do. My vets don't charge for phone calls.
If you have got someone to help, having her tied up with a bowl with food and that person in front of her you should be able to have a closer look (and sniff...
).