W.L.
You can check in a carseat with baggage and a stroller at the gate. Your baby is only 6 weeks old, so I would suggest using a baby front pack carrier instead of a stroller. You can, however, check a stroller at the plane as you board. They will put it off to the side and place it with luggage before take off My son was about 8 weeks old whekn I traveled last year with my tehen 1.5 year-old too. I used a Baby Bjorn carrier and it worked out a lot easier than I thought. He slept most oof the time and my hands were free to help my 1.5 year-old, take off my shoes at security, etc. On one flight, I was asked to take him out of the carrier on take off and landing, but that wasn't a big deal. Because of his young age,he slept most of the time. I was ready to nurse him if he was fussy or hungry, but didn't need to. Just make sure she is fed and changed before boarding and with only you two, it should work out ok. Remember to nurse (with a blanket to cover so no one is uncomfortable if sitting right next to you-you never know who you will sit by) or give her a bottle when she's fussy and you are good to go. Have a nice trip!