H.B.
OK, this is going to sound harsh, but I mean this kindly: what kind of housework is that important that you're up doing it until 1 AM?!?! Seriously, even if my mother-in-law was coming for the weekend, there is no way in h**l that I'm not planning on being asleep by 10 at the latest. That way when my #2 joyously awakes the household at 5 AM, I can at least act alive (after several cups of coffee).
Now, I have to offer my admiration that you're at the gym. You've got me beat hands down there.
Seriously, though, you can't be a good mommy and take care of the baby until you take care of you (and that means sleep)! Pick your priorities; for me it was (1) baby or sleep depending on my recent sleep (remember baby can nurse while you sleep), (2) sleep or baby, (3) coffee, (4) work/pumping, (5) husband (as a big boy, he was a little bit farther down the list than my little boys), . . . (20) housework.
Also, do you have a baby carrier that you wear? Personally, I counted that as gym time and it allowed me to do the laundry, vacuum, have a life and talk on the phone, pick up #1's bountiful toys, cook, etc.
One last thing (that I'm sure you don't want to hear): remember that sleep deprivation worsens depression. Going to the gym to lessen depression is great, but don't let that be at the expense of some shut eye.
You will get through this.