Extra dog slot "safe"?

I use it constantly and hadn't much trouble. The only thing, that sometimes happened to me, was that Dog couldn't heal himself. Normally it was enough to dismiss him and call him again.

I haven't uninstalled the mod yet though

EDS is mostly safe.

Most concerning is that, if installed with other mods that use EventManager, it can contribute to a game-breaking issue where the Redcliffe night zombie battle won't trigger properly. (There should be some discussion of this in the Nexus comments for the mod.)

Other known issues are the party picker screen acting wonky when Dog is summoned; that sometimes a summoned Dog will die and cannot be revived; and 'banter' exchanges between Extra!Dog and other companions not triggering. And for Cousland Wardens, Dog can be locked in the party but non-accessible (i.e. no 'companion portrait', can't be healed or controlled) during the Prelude... thus I always recommend not even installing the mod until after the Warden has at least three other permanent companions. (And IIRC, there are some issues with a summoned Dog being active when Lost in Dreams is triggered, and with Rescue the Queen... basically, any time the party composition is forced via scripting -as with Ostagar - can be problematic.)

As for uninstalling the mod mid-game, yes, that's possible, but note that it's important to dismiss Dog as a summon before uninstalling.