Is this appropriate?
In general and with strangers its best to avoid speculating about others as it can occasionally cause offence or be deemed as inappropriate. However, considering some points in your description:
We are a pretty close team
open with each other at least regarding matters that may impact work
This coworker has had problems with their dogs before
I would say that in your cases, so long as caution is used for understanding when you should instead be discrete, speculating may be appropriate and sometimes even beneficial.
It sounds as though your group would happily share these details with each other anyway and if there is some information she has shared with you openly before then it is safe to say that speculating would not be considered as rudely gossiping behind their back as you are not saying it in a demeaning way and you are not spreading private information, instead the purpose of this speculating is to share thoughts to reach some connection that you may not have realised before and having a most-likely reason for absence can sometimes make a large difference when planning for a project/schedule.
Scenario 1. If your co-worker mentions to the team that she gets intense allergies at the start of spring, but all she has to do is head into the doctors and gets some medication, and if such a thing happened she would be back at work/as good as new the next day. Then a few months later, on the first week of spring she is absent for a day. In this case, even though you are talking about medical information (typically viewed as VERY private) it would be totally appropriate to speculate that perhaps her allergies hit and will be back tomorrow.
Scenario 2. If your coworker mentions to the team that she gets intense allergies to dust. Then one day she mentions to you that she is going to help her boyfriend move into his new apartment and the next day she is absent. In this case, to speculate that she her allergies may have played up due to the dust from helping move the boyfriends belongings would be considered inconsiderate and gossip as it discloses private information she had not shared with everyone and also encourages/leads the way for further speculation from your co-workers about what else she may have been doing at the new house which is not work related and certainly inappropriate.
In scenario 1 your speculation is more piecing together things your co-workers already knew and may help decide if you should make that awkward report to your manager that the project will be completed, just slightly late or to outsource that section of the work. If you use information only you knew then it would depend on what the information is to determine if its appropriate or not. "She did in fact have an umbrella" is a lot less risky than "She ate 3 tubs of ice cream in the break room yesterday". In the end you would have to judge for yourself and it may depend on the sort of people your co-workers are.
In scenario 2, as you can imagine the typical reaction from said co-worker would be to get upset and if this is the case then its obviously inappropriate. However, even in the case where the co-worker is particularly open, sharing similar information freely and would not get upset. While it may not be considered fine/appropriate from her and your co-workers perspective... HR might have something else to say about the matter.
So long as you are mindful of your co-workers feelings and the information has been happily disclosed to the team already, is work related and does not paint the co-worker in a negative light then yes speculating can be appropriate.
