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We did it both ways, the stroller needed to be folded up and placed on the x-ray belt either way when we went through security. Either carrying her or wearing her we went through the regular metal detector rather then the full body scanner. We have pre-check and global entry cards so we don't have to remove shoes or our liquids/electronics so carrying her still worked out, if you have to do the usual tsa requirements wearing her in a carrier would at least leave you hands free. I liked having the ability to push her in the stroller in the airport and have a place to put her while we ate. We gate checked our stroller and it survived the flight just fine. I liked having the stroller when we got off the plane and it was great to push her while we got our luggage and sorted out our rental car.

I've never brought a stroller (never needed one at destination), and so we've used the carrier. I will say though that I've been asked to either take her out at security, or they have to pass the wand between her and me. I've just taken her out and carried her through. It probably depends on who you get.

I've always worn my little through security. Even at 2.5 I still sometimes back carry her if I'm alone so I don't have to worry about her running off.

I've never had to take her out and they just swab my hands. I use a stroller to carry the diaper bag and other stuff so I vote leave it out but babywear the little.

Oh do make sure you don't use a ring sling if you do use a carrier as the metal Rings set off the metal detector

And it will be easy! Traveling with a little baby is no big deal and I've always found other travelers to be really helpful

Here is my very long answer! (It is copied and pasted from this thread: http://boards.hellobee.com/topic/tips-for-flying-solo-with-an-infant which also has great tips)

Last summer I had to fly with my DD 5 time solo. It was a short trip (4 hr flights) but I did my research!
Here are a few of my tips:

-Get a baby carrier! I bought the lillebaby specifically for this, and it has been great. I wanted one that the child could face in or out, especially for the plane ride.
-I had a graco infant carseat with the stroller frame. Get a carseat cover. and if the frame is important to you get a stroller bag too. My frame was damaged, so I can't use the one-handed grip to collapse it anymore. I had no problem, checking them, but they do both need to go through the xray machine at security.
- I really pared down my packing, so I could do it all carry-on. I had one rolling suitcase, one backback, and one pump bag. The suitcase and pump went in the overhead compartment> no packing anything in those I needed during the flight. The backpack (my own personal one, from llbean) has 3 big pockets. This had my wallet, earphones, phone, ipad (ya know all the purse stuff) 2 changes of clothes for the two of us, snacks for me, toys for her, extra diapers and a diaper clutch. (more extra diapers in the suitcase)

So here is how it worked, I wore DD, and pushed the stroller. Security was not helpful, but everyone in line was patient, because you have to put all your luggage through, and take you shoes off (< wear some kid of slip ons!) and then fit the carseat and stroller frame through. I had no help from security but MANY fellow passengers helped. I think it helped them knowing that I knew what to do, and was doing it quickly.
By wearing the baby, the stroller was free, so I piled all my luggage on/under it.
After security, I found the gate immediately, and got situated. I think I let DD down, on a blanket (she wasn't crawling yet) while I resituated everything. I think I fed her a bit if she needed it but I tried to time it so she was nursing during take off. Once we both had a chance to stretch our legs and for me to stuff my face with some kind of snack, I started getting ready for the plane.
I went to the gate attendant, and requested to gate check tags (stroller & carseat), put the car seat in the car seat bag, and then put it back on the stroller (sometimes it clicked in, sometimes it just sat on top). I put my pump bag underneath, and my backpack in the car seat. I put DD back in the baby carrier, and rolled us all into the bathroom. I peed (while wearing her, so make sure what you are wearing is compatible!)
Then changed her diaper, to try to avoid changing on the plane.
After we were all done there, I put DD back in the baby carrier. I put the pump bag on one shoulder, and then put the backpack on. I roller the stroller and the suitcase over to the boarding area, ready for our call.
MAKE SURE YOUR CHILD HAS A TICKET or you child is ON YOUR TICKET! I almost couldn't get on one flight, because my DD's name wasn't showing up on my iPhone ticket!
Ok, so roll to the end of the tunnel, leave carseat, collapse stroller, and head onto the plane.
Suitcase above, pump bag above, backpack at feet.
As soon as I got on the plane, I took anything I needed out of the backpack (water, diaper clutch, toys, snacks, phone, ipad, etc. its very difficult to search for something in a bag in a plane seat with a baby in your lap!)
DD was amazing during the flights, its was a good age. She just nursed and napped most of the time. We walked up the aisles, sometimes just standing in the aisle. We only had to do one complete outfit change on her, some poop leaked up the back of her onsie. Change in the bathroom is difficult, but again, at that age not to bad.

I hope that helps a bit, I know it was a lot of detail. I'd be happy to give more information if you have more questions!!

Oh a few more things I remembered:

-wear pants with pockets you can reach. I had some pants that had a zip pocket right around fingertip length, which was perfect because I could put a credit card, ID, DD's birth certificate, the boarding passes, my phone and headphones in there. (once you are sitting, you can't reach into regular pockets) Make sure your top is nursing compatiable as well, if you need to. I wore a nursing top and nursing sweater.
- DD's outfit. She wore a onesie, with a hooded sweatshirt, baby legwarmers and socks. The legwarmers were one of the best tips I read, because it streamlines diaper changes. All you do is unsnap the onesie to change, no having to worry about pants! (good for diaper blow-outs too.) And with the constantly changing airport/airplane temperature
I could easily adjust her outfit as needed.
-We cloth diaper, but I used disposables on the plane. I did however put a diaper cover over the disposables for extra containment. < Not sure if this applies to you, its not a necessary step, just extra insurance.

@periwinklebee: I'm so glad my tips helped!! Sorry about your travel disasters. I hope the rest of your tip went well.