Ok, so.... why would Janeway move ships? At all?
Did nobody notice there was no Captain of the Dauntless? Janeway is listed as the commanding officer of the Dauntless over on Memory Alpha as well and there is no named Captain, it jumps straight to the Andorian First Officer Tyses, and then the Tellarite Chief Medical officer Noum.
They're also to be non-federation cadets under her direct tutledge so there's little reason for them to move, especially as they went to the expense of introducing these characters. They also seem to have been set up as the proper foils for the rest of the Prodigy children.
Tyses seems very straight laced to teach the command track to the chaotic and frequently incompetent Dal.
Noum could probably teach Jankom Pogg how to be a proper Tellerite or "Federation Royalty" as Pogg would likely continue to insist to the CMO's grumbling.
Also a ship which can operate in Transwarp and thus get to the timey-wimey rift quickly seems the most sensible and the model's already made and ready to go.
Consider that it is possible that the Dauntless, assuming it was repaired quickly, may be the ship that will bring Gwyn to Solum. It makes some sense, considering that Solum must be very far out and thus a vessel equipped with quantum slipstream drive is a logical choice. Tysess and Noum (the latter having some experience working on a Vau N'akat in severe medical condition, which may be useful...) could interact with Gwyn (shared aquaintances include VA Janeway, Jankom and Ascencia), keep an eye on her mission/behaviour and send reports to VA Janeway. Since Ascencia is likely to turn up in or around Solum (potentially in two versions), this would offer more chances at a dramatic confrontation with the crewmates she betrayed.
Granted, it's also possible that Starfleet send Gwyn out on her lonesome on a shuttle, but then she will have to take enormous risks to even reach Solum on time (unless Starfleet has a supershuttle prototype that can also take a superduper warpdrive and is willing to just give it to Gwyn, with a large risk that it will be captured by the Vau N'akat). So I guess that sending her along on a proper explorer, to support and monitor her, would be more logical.
Anyway, VA Janeway stated she will have her choice of ship and it was quite heavily implied it will be the Voyager-A. And if not, it may be another (very) large vessel with plenty of new faces, as it will be a ship where Starfleet cadets (not just the Protogies) will be training on.
The timey-wimey rift isn't even that far out of the Federation (the site of the big S1 finale battle was relatively close to Earth/Sol) and could probably be easily reached by all the regular bigger Starfleet vessels, including the Defiant class (which may just be a smart choice for a mission to future Solum, especially if equipped with cloak).
Because she can. And she will. Because the entire reason why those shuttles were labeled NCC-74656-A is because they’re getting a new ship. This is an animated series. There are no sets or ships that need to be reused.
Agreed on the Voyager-A, but even animated series need to create their assets. Though I'm no expert by any means, I would guess that reusing the Dauntless exteriors and interiors (and associated character models if they indeed use Tysess and Noum again) would save time/money and leave them free to do something else with that money (like creating Voyager-A interiors and Solum scenery). So I wouldn't be surprised if the Dauntless does show up during S2, possibly on Gwyn's mission as mentioned, or else they may still turn up as part of Janeway's group at some point (though it likely won't be the training vessel Dal and co will be on, at least initially).
So? Neither the Dauntless nor the Protostar are good training ships. Changing ships makes sense to me.
Yes, it was implied to be larger and the extremely fast speed of the other two vessels is unlikely to be needed (though Voyager-A may have quantum slipstream anyway, I suppose).