How old is your daughter? Is taking the phone away a viable option? Even with no data, if there is wifi available there are multiple ways to send messages. With tech savvy kids, the only way to ensure no "internet" is with a basic phone or no phone. And even a basic phone can send picture messages.
What phone does she have? Sending a picture via text messaging (MMS) is really quite different than blocking Internet access. Not being able to send pictures via text messaging is quite restrictive and if you feel she needs that kind of restriction is she really ready for a phone? Putting severe restrictions on kids is often like whack a mole, there is so many ways she or her friends will figure out a way around the restriction. I guess if I was in your shoes and knowing what I know about technology I would ask 2 questions:
1) Is she really ready for a phone?
2) Am I being unreasonably restrictive?