Very similar experience, took our daughter for the first time just shy of a year old. We had an Queen size inflatable mattress and she slept between us with some blankets and fuzzy pajamas. She slept like a rock, even better than she does at home.Took ours for her first camping trip at around a year. Overlandish style car camping. She slept between my wife and I on a large air mattress. Worked ok.
Graduated to backpacking trips at 2 years old. She sleeps like champ in her own bag (big agnes duster 15) and on her own pad (nemo tensor insulated). The bag has a sleeve to keep her on the pad, essential with a toddler IMO.
We have a backpacking trip planned in the grand canyon in a couple months.