I suspect your dd has said something further for her to extrapolate so far.
Does she have friends whose parents are separating? I know somone who at parents' evening was offered sympathy on their recent separation.
Turned out their ds' friend's parents were going through a nasty split, and her ds, to show empathy had made up the same-including describing in great detail to the form fights, arguements, visits to dad etc. He was a bit older (about year 3/4) but the teacher was totally taken in. Luckily parents thought this was very funny.
It's also possible she does think you're splitting. Could something have been said during an arguement perhaps that she overheard? "I would be better to walk out now," was something one of my friends heard at school and came to school in floods of tears because she thought her dad was leaving. He wasn't, but she was on tenderhooks for weeks.
The other thing that comes to mind on the description of her, is perhaps formmates' comments "you always want to do everything." "Why do you always have to know the answer?" Could be as far as bullying, but more likely a couple of cross comments about her always volunteering (or perhaps always being picked) has made her want to be less visible. It doesn't even have to have been a deliberately nasty comment, if she's a bit sensitive, a small remark may have been picked up on.
I would have a talk with her. I don't think year 1 is too young to tell her what the teacher says within limits.
Tell her how much the teacher thinks she's wonderful, then ask.
"Miss X says you don't seem to want to answer questions in class much. Is there any reason for it?"
She may not give the actual answer then, but she may come out with it later.
But also if she's not seeing your dh much (and is used to) it does effect them. Dh had three months working where he had to commute leaving before the dc got up, and coming home after bedtime. It effected all my dc in terms of behaviour, both at home and at school, dd1's teacher said she could tell within a week when dh had stopped commuting-she was much quieter (and she's quiet anyway) when he was away.