Is Dorne even in a position to get their forces to King's Landing?
Not unless they also stole Littlefinger's teleportation device, or have somehow managed to sneak an army through the Reach/Stormlands with no one noticing
Might want to keep an eye on Houses Darry
Canonically, House Darry was destroyed by Gregor even before Tywin fought Roose at the Ruby Ford... so it's very possible that's true here as well.
This right here makes it abundantly clear that we have a critical lack of intelligence.
Absolutely. Therefore:
[X] Plan Intelligence:
-[X] Send ravens to Father and the North, informing them of what we know. Ask him to keep a watch on both coasts, and mobilize all he can of the Manderly Fleet (in case the Golden Company decides to land in the North).
-[X] Send ravens to Seagard and any other coastal holding we have, asking them to scout the seas as well as they can, and immediately inform us of what they find.
-[X] Send ravens to Casterly Rock. Inform them of what we know of the Iron Fleet sailing past Seagard south, and advise Tyrion to take Stafford's host and see to his coasts. Also inform him of a possible Targaryen invasion (the Lannisters are their natural enemies, after Tywin's Sack of King's Landing), and tell him we may need his men once the coastal situation is resolved.
-[X] Send ravens to Renly and the Lord of the Reach. Inform them of what we know of the Iron Fleet sailing past Seagard south, and advise them to see to their coasts. Remind them that the Iron Fleet has a shallow draught - if they break through at the Shield Islands, they could sail up the Mander until Bitterbridge. Similarly, they could break through at Oldtown and raid up the Honeywine.
-[X] Send another raven
only to Renly, informing him of an invasion by The Golden Company, carrying Targaryen banners, and supposedly led by Aegon and Daenerys. Remind him of the Siege of Storm's End, where Stannis protected him and gave him his rations, when they were besieged by Mace Tyrell - on the Targaryen side. Remind him the Targaryen's will have no mercy for the usurping Baratheons, and advise him to be wary of Tyrell and the rest of the Reach Lords, who might still be loyal to the Targaryens.
-[X] Send ravens to the Vale Lords, informing them of what we know about Saltpans, and advise them to fortify the Bloody Gate and prepare themselves for the option that the invaders may try to go through the High Road into the Vale (unlikely, but still our duty)
-[X] Send a raven towards Saltpans - maybe the castle of Ser Cox held out? In any case, send a wide but closely connected net of outriders and scouts, aiming to discover what happened at Saltpans, where the Golden Company is now, where is it heading, and what are the forces at its disposal.
-[X] Send Stannis' fleet north, towards Saltpans - if the Golden Company did land there, the fleet could blockade the Bay of Crabs, or even attack it and destroy it, stranding it. So much the better if the ships are heavily loaded with provisions/men/horses/elephants. At the same time, advise them to be vigilant - the Iron Fleet might show up unexpectedly at their rear (who knows how many people stole Littlefinger's teleport machine?).
-[X] March north with our army towards Saltpans, aiming to rest the night at Harrenhall (I assume we can reach it without exhaustion, if we can reach the Ruby Ford with exhaustion). When we get there, set up a strong camp and vigilant perimeter.