I suspect we will trade down.
To make it more interesting I will predict we trade down with either the Giants or the Raiders. In the end I feel the Giants will use their second 1st round pick at 17 or Oakland will use its second 1st round pick (24) or their third 1st round pick (27) for a QB they are interested in, if he is available to the Dolphins at pick 13.
I feel those two teams are looking for, but are not desperate for, a replacement QB and they have the draft capital (multiple 1st round picks) to move up if they see one they want and a trade is a possibility. The dolphins are in a good spot for that possibility at pick 13.
Keep in mind the Giants & Oakland are looking for a developmental QB and may be using different criteria to base their QB evaluations on as opposed to teams with very immediate needs at QB. This is why I think a QB they may be interested in could be available at 13 combined with their multiple 1st round picks which limit their risk in this kind of undertaking.
There are likely to be additions to the 1st round pick in any trade negotiations, but those would likely be 3rd round or further back. I don't see how the Dolphins could refuse such an offer unless they want the player available at 13 more then they want to get an extra pick with only a slight loss of 1st round positioning (13 to 17).
To put more of a point on my prediction my prioritized choices are:
1) The Giants give us their remaining 1st round pick (17), a 4th and a 6th or equivalent(assuming they have any in those rounds).
2) Oakland gives us their third 1st round pick (27) a 3rd, a 4th and a 6th or equivalent (assuming they have any in those rounds).