Basically, the Gogo Travelmate is just an overpriced luggage cart. You can go to Walmart and buy a normal luggage cart, better quality, at a fraction of the price.
You might want to put an extra bungee cord on it to secure it. Play with it at home before the day you fly.
Get one with a metal base. The Gogo has a plastic one which I don't trust. The cart I have was originally used for work, before Flight Attendants had to use those awful rollaboards. It's more than 20 years old and has served me well. I like a telescoping handle but I've noticed that it can really jack up the price. Also, be careful if you're tall. Make sure the handles are high enough to be comfortable.
This is a good way to get the car seat through the airport in certain cases. I didn't usually bring a stroller. When my toddler got tired, he or she could ride in this set-up instead. Won't work for a younger baby though. Too upright.
If you have an infant seat, using a snap-n-go or other stroller frame might work better for you. Then you can place your infant down when not being worn. I did it this way too.
The car seat can also be transported on the stroller, if you're bringing one. This might be better if you're traveling alone. Again, you may have to play with it and you may or may not be able to let the child sit in it. Depends on the model of both items.
If you have the luxury of flying with another adult, one can push the stroller and the other can pull the car seat on the luggage cart behind them.
The best part of using a normal luggage cart is that it can be used for other purposes. You're not buying a travel-specific product. My kids are out of strollers and mine comes in handy for moving things. When your older kid has a big science project that needs hauling to school-you're set!