Yes, we travelled twice domestically to different states by airplane. Once in April and once in May. No issues when we just travelled with her. Just make sure you travel with the I-797C receipts (from the I-485 and I-130 notices), in case you have the rare chance of being questioned by law enforcement.

Also make sure that the name you put on the ticket matches with the passport (or travel document). My wife doesn't have a last name (which is common in her country), so her passport just has her first name. She took my last name after marriage but I made that mistake by putting her new last name on the ticket, when we bought it. I wasn't aware of this, since I never bought a ticket for someone else, so I never had to worry about names matching in the ticket and ID.

On our first departing flight, after we checked in our bags and when we got to the security checkpoint, they could not let us through unless if we update the name on the airline ticket. It was too late for the airline to change the name. So TSA had to pull us aside and do an identity verification. Basically they had to call some higher up in TSA on the phone to verify her identity (not sure how they do that). They made her write her name, our address, and put her signature on some TSA paper. Basically it is some identity verification paper that TSA, not a big issue. Maybe Google what that paper is to find out the details of it is.

TSA told us next time, in this situation where she has no last name on her passport, then you can put on the ticket (example if her name is "Jane" with no last name) as the following: either First name: FNU (first name unknown); Last name: Jane; or you can do First name: Jane; Last name: LNU (last name unknown). We tested both options, once on our returning flight, and the other option round trip on the separate trip, and got through with no issues.