Filling up on formula can make babies sleep longer but because it makes them sleep too deeply and this could be a SIDS risk.
It's also not good to stretch their tummies by overfilling them.
I wonder if there might be other solutions? Is it the bedtimes with the baby that are getting in the way of you spending time with your DD? Would your baby sleep in a sling maybe, so you could spend time with your DD while your baby starts the night off in the sling?
When my LO was a baby we coslept, but we started every night with her sleeing on my chest while I set on the sofa MNing- (I was very much awake! I expect you know sleeping with babies on sofas is very dangerous!)
What I'm getting at is, are there other ways your baby can feel close to you if you're not in bed. At 9 weeks they don't need to have a strict routine.
Then, you say he's not a great sleeper. Is the issue how this is impacting you? Are you cosleeping? If not, could you look at cosleeping following the guidelines for safer cosleeping, or getting a 3 sided cot that attaches to your bed? We had one of those and it was great. I'm thinking maybe if you can minimise the time you have to spend getting up maybe that will help?
How many times is your baby waking up? It's totally normal for them to wake lots at this age. (You probably know that). People who say their baby is sleeping through are often lying IMO! (You probably know that too!)
Did you just want to have a couple of drinks or get drunk?
If you just want a couple of drinks, there's no harm in drinking while pregnant. All that stuff about pumping and dumping is nonsense. Your BM is made from your blood. It's already been through your body. Even if you were totally shitfaced, your milk wouldn't be any more alcoholic than orange juice (which is very slightly alcoholic, but such a tiny amount that no one ever mentions it).
If you want to get smashed, obviously that would be a risk to the baby though! Not from your milk but risk of dropping the baby etc.
But if you just want to have a drinks or two with a meal or whatever, there's no need to worry (unless you're likely to get drunk from 2 drinks!).