I got here through who_daily and am probably doing to ramble for a bit, so sorry in advance for that! :)
My thought is really that they would not have daemons at all, not even invisible ones like the humans of Will's world. I really did read the books as saying daemons were totally unique to human beings and that every other species of sapient beings had its own way of connecting to Dust - the Panserbjorne don't have daemons, the Gallivespians don't, the Mulefa don't. Time Lords may look human, but they're still different from us, and I don't like skimming over the difference like that.
(Of course I also don't think daemons really were peoples' souls, but that that was just the explanation the humans of Lyra's world had come up with for their existance due to not knowing what was really going on...)
If they did have daemons, I think there's a good chance they'd settle as animals we wouldn't recognise at all. Though that poses the question of what even limits the forms someone's daemon can take - can they take a form the person has never even seen? It seems a bit weird, can you imagine some poor medieval villager's daemon becoming a platypus and their peers' reactions to it? If it's only limited by known animals, than presumably the Doctor's daemon at least could take the form of an Earth animal, but would not necessarily, if there was something that fit even better out there. I also do think that yes, it'd change with regeneration (or else it wouldn't even be an issue, they'd settle before they ever left Gallifrey, end up with a Gallifreyan form and that would be that). They'd probably be unsettled for a bit while the new incarnation was stabilising - so Ten's daemon would not have a fixed form during The Christmas Invasion, for instance - before taking a new permanent form.
Finally, I actually have written a ficlet (http://katflace.livejournal.com/556693.html) that plays with this a bit, if you're interested. Probably the reason I've thought about this so much, heh. I've wanted to write more bits from the same world - for instance, surely Three would've needed some way of creating the illusion of having a daemon, if he was going to interact who didn't know he wasn't human during his exile? - but I've never gotten around to it so far...
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My thought is really that they would not have daemons at all, not even invisible ones like the humans of Will's world. I really did read the books as saying daemons were totally unique to human beings and that every other species of sapient beings had its own way of connecting to Dust - the Panserbjorne don't have daemons, the Gallivespians don't, the Mulefa don't. Time Lords may look human, but they're still different from us, and I don't like skimming over the difference like that.
(Of course I also don't think daemons really were peoples' souls, but that that was just the explanation the humans of Lyra's world had come up with for their existance due to not knowing what was really going on...)
If they did have daemons, I think there's a good chance they'd settle as animals we wouldn't recognise at all. Though that poses the question of what even limits the forms someone's daemon can take - can they take a form the person has never even seen? It seems a bit weird, can you imagine some poor medieval villager's daemon becoming a platypus and their peers' reactions to it? If it's only limited by known animals, than presumably the Doctor's daemon at least could take the form of an Earth animal, but would not necessarily, if there was something that fit even better out there. I also do think that yes, it'd change with regeneration (or else it wouldn't even be an issue, they'd settle before they ever left Gallifrey, end up with a Gallifreyan form and that would be that). They'd probably be unsettled for a bit while the new incarnation was stabilising - so Ten's daemon would not have a fixed form during The Christmas Invasion, for instance - before taking a new permanent form.
Finally, I actually have written a ficlet (http://katflace.livejournal.com/556693.html) that plays with this a bit, if you're interested. Probably the reason I've thought about this so much, heh. I've wanted to write more bits from the same world - for instance, surely Three would've needed some way of creating the illusion of having a daemon, if he was going to interact who didn't know he wasn't human during his exile? - but I've never gotten around to it so far...