Doesn't matter about the surnames. Me and DD don't have the same name and I fly/travel alone with her frequently. How long is your flight? Hopefully your DD will sleep. If she uses a dummy, give it to her on take off and landing, otherwise feed her. Babies eustacian tubes are tiny and the change in pressure can cause pain. My best top tip though is enjoy it. Babies are much easier to fly with than nosy toddlers.
bagel I have been advised to always take the birth certificate (copies) when travelling internationally with my dc (different names as well), I have the bc stapled into the back of the passports so that I don't lose them. depending on where you go it might be usefull to take a copy of the marriage certificate as well + a letter from your partner (if not married) that he agrees to you taking the dc abroad. give your dd drinks during landing and take off. oh, and get a sling/carrier. you will only get the pushchair back with the luggage (after immigration!) at most aiports.
It depends where you are going, for example the US immigration suggest if you are travelling with just one parent (even if the same surname) you carry a letter (preferably notorised) from the other parent or another document to show you have the right to take the child out of/into the country. However I have travlled with two of mine with no such document and no problem.
When travelling alone with DS (intra-EU), I took his birth certificate with me, but no-one asked for it.
Definitely take a sling/bjorn something, it's helpful on the plane as well so you can have your hands free.
Are you taking a car seat with you? If yes, ask at check-in if the flight is full. If not, they may well let you take it on board. It happened to us a couple of times and it was great, as DS slept in his car seat for the whole journey.
If you're not bf, take more formula than you think you'll need.
Have lots of wipes at the ready, because DD WILL poo the minute you're buckled up and taxiing.
regarding again the birth certificates: I found that this year the passport checks have been much more thorough than before. even my 4yo has been questions (is that your mommy? what is your name?) by the passport officials and they specifically asked to see the birth certificates.
another one: take an extra t-shirt for you in the hand luggage. my dc had a tendency to be sick all over me when they were little. (not it's only chocolate handprints all over)