Deep sky astrophotography (AP) is certainly possible with a goto dobsonian. There is a 12" goto dob for sale here & the seller has included pics they have taken with said scope:
https://www.iceinspace.com.au/forum/...d.php?t=214716
While tricky for DSO's, imaging the Moon & planets is much easier with an altaz mount, especially if it has goto/tracking as the exposure times are very short.
The learning curve in AP is steep. The scope is the easy part, the trick is the mount & camera, the mount in particular as there is a relationship between scope size & mount for stability & tracking accuracy. There are also technical aspects with scopes that mean more bits & pieces are required to produce pinpoint star images across the field of view & which astro camera... Then comes the image processing. I'm saying this not to bamboozle you but to make you aware of expenses to come so you are not just writing a blank cheque
If you go with something like an 8" goto solid tube scope (if there are such scopes) or a solid tube dob it will be a standout instrument. I say solid tube because these can then be coupled to a suitable equatorial mount for more serious AP if your daughter wants to. It isn't doubling up as a dob is much easier to do visual with.
Alex.