Great news rocket. Keep it up, and remember that though there may yet be setbacks, you CAN do it.
Your DD being so small though, if you get worried, trust your instincts. In those early days there are things that might be going on in the background causing your baby's sleepiness, like an infection, and if untreated, things might get bad very quickly. We went to A&E because DS 'wasn't feeding right, and was sleepy all the time'. They took us seriously, we were seen immediately, no waiting, they said it was absolutely the right thing to do. Turned out that all he needed was top-ups due to messed up supply, due to earlier problems (he had had an infection at birth). However a friend's DS wasn't feeding and she just felt things were not quite right and it turned out he had a serious infection. Not meaning to scare you, just saying trust your instincts. That works the other way too - if people are telling you that you must feed your DD more, that things aren't ok simply because she isn't feeding every 3h, but your instincts tell you that actually, things are fine, then don't let people create unnecessary pressure for you. Remember, you know your baby best.
Some tips for now:
I found that to get DS to feed, we both had to be calm. Sometimes that meant letting the 3h 'slot' pass unused, waiting for the right moment. Sometimes it meant I had to be completely alone. Sometimes it meant I needed DP to be there, to carry DS around and bring him to me, then lift him to the other side, so that I didn't need to faff around.
Warming up your breasts is good for before feeding too, not just for before expressing.
Drink lots. Seriously, not drinking enough WILL limit your supply. And I second the fenugreek (you can buy capsules at Holland&Barrett).(But avoid mint tea, and sage.)
As much as sleeping in the night would be lovely, try to feed and/or express at least once between 2 and 5 am. That is excellent for keeping supply up. If you want to skip a feed, choose an early evening one instead.
If your breasts are engorged, it can help to hand-express a little off before starting BF.
And now some points for later, when/if you try to get your DD to breast only again:
Introducing something new such as breast only rather than bottle, works best when baby is NOT ravenously hungry and upset. DON'T think 'oh when DD is really hungry, she will feed' - when she is very hungry, she might be too upset or too weak to feed properly.
We were advised to drop one bottle-top-up at a time, not all at once. It meant longer hard work with expressing and bottle feeding, and every time we dropped a bottle, DS would be hungry all the time, but it worked. We did bottle top ups after every feed from 2.5 weeks until 4.5 weeks but by 9 weeks we were bottle free.
Oh and a reassuring story: You asked if you had ruined BF. Well a midwife tells the story of a lady who had her baby prematurely in France, at the time it was customary in France to give preemy mothers the injection that stops your milk coming in. She went to see said midwife when her baby was 8 weeks old, fully formula fed, and sad about it. Boy was she surprised when told she could still BF! With some work she got lactation started, gently got her baby used to the breast and weaned off the bottle, and at 5 months the baby was fully BF. The point being, your chances are never ruined. Perhaps things are harder now than they needed to be, but losing your supply because of 'having done it wrong so far' is never inevitable/irreversible.
Good luck!