Op I’ve traveled a lot with Newborns to visit family. Important to note most airlines allow two pieces of baby equipment as standard (is 2 travel free).
The first thing to consider is accommodation and your sleeping plan/preferences - for example, there are cribs that fold away that function as “next to the bed” set ups (ie the folding crib) OR prams that are for safe sleeping that could be left within bed touching distance. If bringing one of these, pack as many extra blankets as possible into the package as they are brilliant to cover surfaces to make safe spaces to leave the baby down (ie in a bathroom so you can shower etc). Not needed for a 6 week old, but for an older baby bringing the cot sheet from their bed at home and a gro blind helps my kids accept a hotel travel cot!
Clothes wise, it will be hard to plan until you know your baby! Each one is different. With my 3 week old I’m currently needing at least two “outfits”/full changes a day (due to poo or spew) and yet am fine with one baby grow overnight. I’m using two Muslins a day but they wash in a sink and dry quickly. I’ve two ikea rubber backed change mats that fold down to nothing. One lives set up in the room we sleep in, and the other in the change bag. For £4 each (or something similarly cheap) they protect the bed from baby mess and make my life as a mom a LOT easier! Having two means one can always live in the change bag.
I’m currently away and didn’t pack enough for me! Big knickers, feeding bras and non disposable breast pads (the disposable ones make me ich) are all stuff that frequently stain/get wet and although they hand wash ok, I underestimated that i could get through more than one change a day! And don’t like having such items drying on display. So wish I had more for me!
Will you need a car seat, a pram, a sling and something to sleep in? How can they be combined to best pack for travel. Presumably it’s three bulky items so one will have to be paid for? Buy a “storage bag” of Amazon for the pram or car seat - pack nappies and wipes into that to pad it out - this Keeps it safe for travel and removes bulk from your own packing. Again once baby arrives you’ll have a better idea of how many you’d need but I would suspect at minimum 2 packs of wipes and 80 nappies.
If it’s somewhere sunny I’ve also always found it invaluable to pack a fold away spf 50 baby tent. (Again probably unnecessary if you plan on bringing a pram, but I often travel with just the sling, and it means I have somewhere safe to pop the baby down)
Passport wise you are under huge time pressure to have it issued. Register the baby ASAP and I suspect you may need to ring the passport office and explain the family urgency to travel. I’ve had to do this and had documents issued within timelines BUT it meant multiple days of cross city appointments in person to sign and collect docs - so be prepared to sort in advance and expect some hassle.
If traveling long haul post chance of a c section etc. think about your own comfort, can you book an extra plane seat? Ring something comfortable to sit on! How will you manage all of the suitcases and equipment each side in the airport, can you pay for a porter or assistance service?