Messages within the same account

For your further consideration, in addition to ‘Family Sharing’ you might also want to consider using ‘Screen Time’ as well (includes restrictions and accesses) and the following link will explain this in more detail https://support.apple.com/en-au/HT208982

I would like to message her, as I work away from home. Do we think this can be done without disrupting the current log-ins, etc,

You could message her though from your non-Apple phone as an SMS. You can send a message to "yourself" from your Mac which she would also on her iPad and you would see also on your Mac's Messages. Confusing, but it would work but it's sub-optimal.

or is it a case of setting up her own account, or a secondary one for me?

Yes, and sooner or later you are going to have to tackle this - and believe me, earlier is easier. I'm guessing your Apple ID is an email associated with you and one she would not want to retain, so the obvious action is to create a new Apple ID for her. This would involve a slight hurdle in your daughter sending a new ID to her mates but it's a momentary inconvenience for a long-term gain. Her new ID would also be her FaceTime ID for video and audio chats an all the other services Apple offers.

She would also have access to the services and content purchased on your Apple ID via a Family Sharing group. See here.

Hi edbevan, thank you for using Apple Support Communities for your enquiry.

Apple recommends that you do not share your AppleID but instead create a AppleID for each family member and consider setting up ‘Family Sharing’ as a better option. The following link explains this in more detail https://support.apple.com/en-au/HT204976

Apple further explains how to Create an AppleID for your child. Please go to the following link https://support.apple.com/en-au/HT201084

The issue with you messaging your daughter using the same account is going to be difficult because all her friends will see your messages and secondly they will know you can see their messages which may create an uncomfortable situation for you, your daughter and her friends.