First time travel just my toddler & me

We're going from Sea,WA to Ont,CA with a 45 minute layover in San Jose. I plan to check our luggage & the stroller. Then put our Graco Extended 2 fit on a dolly that I haven't purchased yet ( any suggestions on dolly's that are airport friendly on Amazon & will fit my seat then fold for over head cargo once on the plane are appreciated ) will the seat fit comfortably? From YouTube it looks like just a seatbelt install. Anyone used this specific seat on a flight as well? I also have a Cosco kids easy elite slim all in one, that I was going to bring it's just not my preference on seat, I know it's lighter and not as bulky as the Graco. Opinions? Am I crazy for wanting to bring the seat on the plane to even begin with? I originally thought the seat was for safety although I've been reading & it seems to be more for comfort & some protection. Advice? This is like my second or third post. My toddler doesn't love her seat in the car normally although she's still rear facing at 2 1/2, 24 pounds. I figure she might like being forwards. Thanks in advance for any help!