You've gotten a lot of advice already, so I figured I'd throw in my two cents, which you can take for what it is worth. A little about me, I am a mom of five kids, all breastfed for at least a year. Since I was never able to sleep while one of my kids was upset/crying, I never used the CIO method. Instead, I always reminded myself that the sleeping "problem" would eventually resolve, and that since I had more coping mechanisms than my babies, I would figure out a way for everyone to get more sleep. And sleep is very important for me, and any new mom too! While no one has said it yet, it deserves to be said that any habit can be broken, so don't beat yourself up over "bad" (whatever that means!) sleep habits for a baby. Everyone wakes up during the night, and eventually everyone figures out how to soothe themselves back to sleep. Your kids have a lifetime to become independent, so you could cut them some slack during the first year of their lives and allow them to be dependent on you, for a little while at least.
If the baby is sick, then have a doctor handle the illness and/or wait for the baby's body to get better. Since I always like to be comforted when I am sick, I always figure my kids would like comforting as well. Therefore, you need to decide how to comfort your child while getting more sleep. Now this could be considered controversial, but remember, this is your family and your household, and whatever you decide to do needs only be known by its members. Lots of folks brag on CIO, but lots of others quietly go about doing whatever WORKS for them. Ultimately, taking care of yourself and getting enough sleep to function well trumps your perfect mommy image. If you get some sleep, that idea will make perfect sense (tee hee)!
As for practical considerations, have you considered nursing while lying down in a bed (not necessarily your bed)? That way both you and the baby will get some rest while the baby gets nourishment and/or comforting, or what she needs. Even if you can't/don't want to sleep with the baby next to you in a bed, you could always wait for her to go back to sleep then transfer her back to her crib. The baby will go back to sleep sooner if she gets to nurse, lie down and be near her favorite person all at the same time. If you wait for her to get all keyed up with crying, the soothing will take longer and you'll get less sleep. My kids always nursed more when they were sick, having a growth spurt (to be expected, albeit rather short-lived), or facing a new situation (like a move). This phase will not last forever, and as she gets older, she will sleep longer -- trust me, they all do!
Secondly, and again, this could be controversial to the super mommy sensibility, during my kids' first year of life outside the womb, I operate on "mommy mode" especially since I am at home during the day like you are. Mommy mode means I don't have to be a sparkling intllectual wit or solve complex world/business/life problems during the day; instead I can focus on things like laundry (which I could almost do in my sleep at this point), feeding my kids, playing pat-a-cake, watching Dora the Explorer/pre-school shows (a great time to take a refreshing twenty minute nap on the couch while the kids are cheering Dora on/ "developing problem-solving skills") -- you get the point. A SAHM's work is a marathon, not a sprint, and you're on-call 24/7, but the work is fulfilling and rewarding, even if not intellectually challenging. Bottom line: you don't need to employ your genius skills for mothering, so don't worry if you're a little tired. Take naps when you can, and relax and enjoy this time with your babies. The rest of the work will be there and you will get it done when the nighttime restlessness passes AND this too shall pass! Besides, the prolactin (hormone responsible for milk production) is going to make you feel "muzzy"-headed, but also more relaxed. God knew when He designed us what we would need to do as mothers/nurturers.
I'd hate for you to give up nursing when you're so close to what will likely be a natural time for weaning. All infants soothe by suckling, and mommy's breasts are the preferred method (for most infants anyway -- IMHO), but you could always substitute with a pacifier if that is what you want to do. No one needs to know exactly how you soothe your babies. That is your business. If the baby is really hungry during the night, then feed her (solids or milk) closer to bedtime and see if that helps her sleep longer. If she just wants some mama love, then decide whether you want to give it to her or help her wait until you're ready. As for my lying-down nursing suggestion earlier, I would just qualify that by saying you probably don't want to do this if you (or anybody sleeping in the same bed) take anything that would impair your ability to wake up (for example, alcohol, sleeping pills!, cold medicine, other drugs, etc.). You obviously want to have all your faculties when you're lying down in bed with your baby.
Finally, I'd just say to do whatever works for you and yours! If you have a nosy person who needs to know everything about what goes on in their household (and you don't want to lie to his/her face), then simply smile, nod and say things are going along as well as could be expected. Everyone learns how to sleep and get back to sleep eventually (my oldest, the 11 year old can sleep through anything, and has been for YEARS)! Remember, the pediatricians define a baby's sleeping through the night as sleeping for (only) a five hour block of time. You, however, can structure your and your kids' sleep time however it works for you. You can institute a daily nap/quiet time, during which everybody sleeps, including you. Conversely you can limit daytime sleeping for the baby in order to tire her out for a longer sleeping stretch at night. A bedtime routine is nice if it works for you, but it doesn't have to be a slavemaster. Kids need to learn to be flexible as well as independent. So, in the end, do what works for you and your family, and remember, nothing about this time of your baby's life is permanent. You're her mom, and you get to guide her through this stretch of her life. Enjoy it while it lasts!