I am an expert at traveling with a young one by myself. Yes,a stroller is absolutely necessary. And you can take it all the way to the gate.
If going where it may have snow get a stroller cover. I had snow stuck in my where it connected and the stroller collapse with baby in it. Scared us more than anything but then i had to borrow a pen adn pick it out for a bit.
Don't fret about security. Some airports have a separate line for strollers so you don't have to wait so long. Also, there is always one security person before the metal dector to help out. Or the people around you I found are very helpfull. I have traveled with an umbrella stroller and then a big one from my travel system.
I always pack too much, being prepared has come in handy a few times, so I like the bigger stroller personaly. Plus having the drink holders was nice. I dont feel so much like a pack mule. I would have a backpack and then another bag size depending on if we were traveling during winter and delays could be a problem.
Here are some travel trips:
1) Put toys on a loop of ribbon (like a toy necklace)so you can attach it to the stroller via tray (not tied to it,)or around your neck when collecting everything to get on/off plane. THen you dont have to worry about dropped toys.
2) Target or Walmart has disposable changing pads so you can cut down on the size of stuff needed. Also, the scented bags to put the diapers in as you wont believe how the bathrooms stink so quickly even from just a pee diaper.
3) If using formula try putting in little bags that can be found at Target by first years. Look in bottle section. The bottoms rip off and right into bottle. Easier than carrying can.
4) Slings can help save your arms and make trying to pull your pants up after the bathroom much easier. I am always afraid to let strangers hold my kids.
5) Dont forget to bring some new toys and lovelys
6) Dont worry if baby cries, everyone understands and has been there.
8) Pacificers help with ears adn the take off. I never needed it but had one just in case. The first time we flew, she was 6months then.
9)Bring a change of clothes for yourself. Wearing spit up for the long flight is no fun. Also, having the baby there can cause a few spills too. My daughter made me spill coke on to my seat, thankfully i had some pants to change into.