Shelby,
First, CONGRATULATIONS, and WELCOME!
Second, great advice from everyone, as usual -- especially planning how you will handle your luggage. Don't be embarrassed or too proud to ask for assistance, including putting a carry-on overhead. (I was embarrassed and too proud at first for I took my first 2 trips -- you know about us men, right? -- but I then thought about the possibility of ending up with an incisional hernia, and asked for assistance my entire trips.)
Third, additional advice: wear varicose-vein-reducing knee-length support hose: Even at 4 weeks post-op, your body is still at higher risk to develop "deep-vein thrombosis" [= blood clots] in the inner larger veins of your legs, especially starting in the veins of your calves. That can lead to a large blood clot breaking free and lodging in your lungs. Not good to have happen. Longer airplane trips as well are a proven risk factor to develop that. As Sherri posted, get up & walk the plane, at least hourly. IN ADDITION, I suggest wearing a good pair of to-the-knee tight, fitting, elastic support hose. "Jobst stockings" [brand name] have been what MDs usually prescribe or recommend, but they are much more expensive than "Futuro" that are at least just as good if they fit you. "Futuro" is the brand name in the US; Futuro has a few other stocking that are not designed for this function, but [as I recall] has 2 types that are designed to manage "varicose veins." They come in different sizes, so measure your knee-to-heel length and also the circumference of your calves at its the widest point [better yet, bring a tape measure with you]. Most large pharmacies carry Futuro at least, & some Jobst as well. I wear mine now every time I take an airplane flight, because age is yet a third proven risk factor. [& no, I neither have stock nor am paid by either company!]
Safe travels!
Bill