Tips for traveling with infant

Me and my 2 month old son will be traveling alone on a two hour flight in a month. He’s a pretty good baby for the most part doesn’t cry much at all. How should I travel through the airport? I don’t plan on taking a carry on bag just a diaper bag which is a personal item. Baby will sit in my lap on the plane as well.

Should I wear him through airport security? Do I need to take him out of the carrier to go through security?

What about the stroller and car seat? Do I check that with my bags at the front or leave it at the gate?

He’s breastfed so I’m not worrying about bottles and water, just walking through the airport and security.