We're currently playing Minecraft at on a server I'm self hosting which is nice, but I'm thinking what next? I don't really fancy her being exposed to the wider internet yet, voice comms etc. What else is there? Quake 3 is my next choice 

A nice RTS game maybe?
It Takes Two is an awesome game. It far exceeded what I expected.
I imagine an 11 year old would like it.
Great list.lego games
zero-k/betond all reason @Journey maybe? / Read alert 3 has a co-op campain
once we were here
golf with your freinds
mindustry
factorio
possibly streets of rogue
boarderlands
dungeeon defenders
ark - maybe or something similar. palworld maybe
Demeo
hacktag - but mixed reviews
keep talking an nobody explodes
left 4 dead
plates up
over cooked
trine
Stardew possibly
I echo all that about It Takes Two and just to add, it also has a lot of longevity.It Takes Two is an exceptionally good game that works really well in co-op. I played it with my 9 year old; be warned there is one section perhaps halfway through or just after involving a toy Elephant that maybe you might want to research beforehand and play through solo rather than expose her to it. I think technically it's a PEGI 12 game, it deals with some subjects that might be sensitive to some kids. But the production values are really high, lots of nice little jokes, puzzles you work together to solve via experimenting etc, good variety of levels / mechanics. I'd say it's probably the best game I've played released in the past 10 years (admittedly, I play far fewer games than I used to). Certainly, as others have said, it massively exceeded my expectations, I've been gaming since the 80s I'm struggling to think of many games that have [pleasantly] taken me by surprise as much. I never would've played it if I hadn't been researching co-op games to play with my son. It's like, they've taken a concept that would be easy to mess up with bad execution or design decisions, wrapped it around a somewhat questionable plot, and somehow absolutely nailed almost everything, it's like a rollercoaster-ride (literally in some cases) where you laugh, cry, feel super conceited and smart, feel like a complete dumbass, get caught off guard, see things coming, go and eat a meal and be desperate to get back to the PC etc etc. I don't think I've enjoyed a co-op game that much since I carted the family PC down the road to play Doom2 over serial link cable with a friend about 30 years ago.
Lego games are great fun although I wouldn't play the very early ones as they are a bit clunky controls wise. Many many hours of gameplay in those, one nice thing is if your daughter likes just messing about in freeroam, you can do mini-objectives at the same time to stop yourself getting bored.
Moving Out is a good laugh, has a kind of Overcooked vibe to it.
Streets of Rage 4 if you liked the old ones.
Trine games if she enjoys small puzzles.
Deep Rock Galactic