Dol Amroth is considered a capital / hub (star icon on the collections tab), but store bought stable master doesn't have it on the list.
I think that i saw it at the housing stable master. Maybe was at the 1 of the public area, or maybe it have to do with the toons level that you used to interact with the NPC. Either way, it is good that the area have a permanent "Return to" port skill that you can barter at that city, very cheap, only gated by a bit of reputation that is easy to raise with a few quests even by tasks.
The homestead is on the list and from there you can take the horse to Dol Amroth.
There are a lot of hubs not on the stablemaster, but it has South Bree from where you can get most connections. If at a premium house, you basically have a lot of return skills since cds on both are very low.