Be vigilant if you use a stroller bag with a gate-checked stroller. There are restrictions on what sort of luggage may be legitimately gate-checked, as opposed to situations where you make it all the way to the gate with a too-large carryon bag, and the FA calls you on it and makes you check it.
Be sure that the tag that gets onto your stroller bag says clearly that the bag should be delivered directly to the gate, and then, when you land, ask the ramp agent if you do not see it right away. Because the wheels are not visible when a stroller is in a full bag, it is possible that the luggage handlers will assume that it was a last-minute luggage check and send it to the carousels; they look first for things with wheels when they look for things that need to go up onto the jetway.
I use a stroller sleeve, rather than a bag. It is a ripstop nylon tube that lets the handles and rear wheels stick out, so that I can pull the folded stroller behind me down the jetway. Even with the wheels exposed, I still sometimes have trouble with the handlers not noticing it right away. The sleeve is bright yellow, so if I tell them to look for that, they always do find it quickly when they look again.
One piece of advice if you decide not to use a cover. Take off all the loose parts of your stroller when it is gate-checked, including any toys, and the hood (I put the hood in my checked luggage.) Fold it yourself at the end of the jetway, and it is best to put some kind of strap around it to secure it shut. (The majority of strollers that break in transit get broken when the handlers accidentally grab the latch and unfold them, then force them shut again, because they don't have time to figure out the fold mechanism.)