There is nothing at all to suggest Dhanush is capable of, or ever intended, to target ships. Or land for that matter if speaking of intention.
SRBMs of this type are effective against air bases, ports & major infrastructure only when launched in salvos of AT LEAST 5-10 missiles, taking into account that some of them will inevitably fail to reach the target. No way 1-2 missiles with conventional payloads launched from ships can have any substantial effect. To strike at moving targets like ships you need two things:
a) highly maneuverable RV
b) a short flight time i.e. high velocity boost stage
The Prithvi (and by extension Dhanush) has neither. The Prithvi RV was designed in the 80s and changed little since then (other than in terms of various explosive payloads developed for it), and that means it preceded the first Indian MaRV (Agni-2 in 90s). Secondly, the fact that it uses a liquid-fueled booster means it simply cannot achieve the kind of ascent & boost-glide velocities that solid-fueled missiles can attain within the same amount of time.
The way I see it, the Dhanush had simply one purpose. To serve as a target missile for BMD tests by launching from the deep sea (beyond the distance where one could reasonably drag a pontoon) and allowing AAD/PAD ABMs to intercept over the ocean, alleviating the risk of debris falling on land (and also allowing ABMs to function as they would against enemy BMs launched over the same distance as they would in war time).