Totally agree with absolutely everything mimbleandlittlemy has said.
I would say to the OP, is your DD 100% aware of the realities of the industry and does she have the kind of personality that you need to survive it?
I have a DC who is a reasonably successful child actor now in their early teens. They have good credits and are with an agent whose high enough tier that their name can potentially open doors. It's still incredibly hard to find work. If you land 1 job every 50 auditions, that is probably pretty good odds.
There are huge numbers of people wanting to do this and drama schools churning out thousands of new hopefuls every year into an industry that realistically only has a handful of jobs available.
Does your DD understand the process once you've managed to get your headshots and your showreel and your agent?
I have people ask me if DC's agent sends us scripts to choose from! Nope, you sit and pray the email pings at least once a week (the last 2 years you prayed it pinged once a month), and then you have anything from 12 hours to maybe 3/4 days to learn whatever role has come through, tape it all and send it back. Tape then vanishes into the ether and 99.9% of the time you never hear another thing. You don't even get a 'no thank you' 99% of the time. In 8 years we have had feedback twice from casting.
If you do hear back for a recall, you can then face weeks or months of call backs, chemistry reads, directors zooms/meetings - and then it's a no. You've committed to the role, dreamt about it for weeks and it all vanishes in a second. You can even book the role and have them change their minds after that! And you have to be able to take all those knocks and disappointments and still get up the next day and put the exact same enthusiasm and excitement into the next role.
With some casting brackets (female 25-30 for example), Casting Directors can receive literally thousands of submissions for a single (small) role. In order to be one of the handful who are selected just for a first tape you'll need to tick an awful lot of boxes - have a specific look, or be with a top tier agent, or have a great cv of previous work. But you can't get that great cv without opportunities and you can't get that top tier agent without the great cv or being the stand-out in your year from a big name college, so it's a huge catch-22 for the vast, vast majority.
Alongside that, as an adult you'll also be having to support yourself in the kind of job where you can drop everything for an audition or to go off and film for 6 weeks. You also need to be paying for constant continual training to keep your skill set up to date and ready to go. Plus your headshots, Spotlight, Equity, IMDbPro.
I once sat and compared costs/time with a friend whose kid is into showjumping... she had to deal with more mud, but otherwise it was pretty similar.
Think very carefully if they have the resilience and rhino hide to take the relentless rejection that is the norm. And whether the level of debt they will take on with a degree course is going to be worth it - and in my opinion it is definitely not worth incurring the debt to go somewhere that isn't a college with a really good name. If your child just wants to perform, there are much easier ways and much more fun ways than doing it professionally.