My son is 4 months old as well. He doesn't sleep through the night either. I put him down at 8 or 9pm and he wakes around midnight and then again around 3am and then again around 5am or 6am for the morning. He will go back down for a nap in his swing around 8am.
He was sleeping from 8pm until between 2am and 5am for about two or three weeks and I was in heaven, but for some reason he reverted back to his old ways.
I would try to put her down early anyway. She may suprise you. You are obviously still up and it doesn't matter anyway.
Have you tried some cereal. Sometimes it works and sometimes it doesn't. My son is eating cereal with no problems. When I started him on it he started sleeping for the long periods I mentioned before, but after two or three weeks he stopped.
My oldest wouldn't sleep through the night until she was nine months old or so. I finally had to let her cry it out for three or four nights. I would let her cry for 10 or 15 minutes, go in pat her bottom and sing to her and then leave for another 10 or 15 minutes until she finally fell asleep.
My second child was much easier. She was three weeks old when she started falling asleep at 7pm after a feeding. She would wake at 11:15pm when I got home from my part-time job and then again around 5am. Then she would sleep until 7am or so. She just got better and better about sleeping the older she got. I never had to train her to do anything when it came to bed time. I would feed her and lay her down and she would stick her bottom in the air and go to sleep. To this day (she's three now) she will lay down at bed time and go right to sleep...almost before you can get out of the room and that's between 7:30 and 8pm.
My third child has been a challenge. He's four months old and can't makeup his mind what he wants to do. He's high maintenance. I'm glad that I stay home. If I had to work I would be pulling my hair out. You may just want to think about how much it is costing you in daycare, work clothes, lunch money, gas money, and sleep to work fulltime. Is it really worth it? My neighbor was going in the hole when we sat down and figured out all the expenses associated with working.
I find that I am still a little tired because I have to get up and get my oldest ready for school, but I'm less stressed because I don't have to get myself ready until I have a moment. I don't have to rush to drop them off or pick them up. I don't have to stress about what to feed my family and how quickly I can get it cooked. I don't have to stress about getting them all bathed and ready for bed so I can clean house a bit before I go to bed.
Just think about it. If you can't stay home then you may have to just tough it out for a few more months until your little one matures a little more and decides she can sleep all night without eating. Remember she will go through spurts even when she does start sleeping when she grows.
Good luck!!