We have done this on DL when Mr. Cellisttoo was on a separate flight from myself and the toddler (and I had enough to handle with the toddler, car seat and two carryons).

I would recommend gate checking it. You just wait until the gate is fairly busy and then go up and tell them that you want to get a gate check tag for your stroller.

However, be aware that DL no longer takes responsibility for strollers gate checked or otherwise. It needs to be in a "hard case, such as a box" before they will cover any damage. Since DL has demolished two of our strollers, I can confidently say that destruction is possible.