That would mean that he pulled out of the gas station with the tailgate up, drove the baby for awhile trying to get her to sleep OR went and to dispose of her body, and somewhere along the way (the trip he claimed not to remember) he realized he could be saving on gas money if he put his tailgate down, so stopped to do so. In the first scenario that would be weird. In the second scenario it would be callous to a point of sociopathy, which I guess in this case would be in keeping with his other actions. Yuck.
i feel that he killed Ember, wrapped her in something (blanket, etc) and put her in the back of the truck. He did not want to drive with her body next to him. He planned this -- that's why he brought the shovel. He found a place, put the tailgate down, took her out and buried her in a shallow grave. His agitation was too great to think of the tailgate again. Driving back he realized he still had her pacifier and lobbed it out the window.
This is horrible to imagine but I feel it is what happened.
I would like to see a cadaver dog go over the truck but I don't imagine law enforcement has much interest in that now that MG is dead. Though at least it might help to establish Ember is not alive any longer.