I think you would be fine on most of the mass market lines, honestly. We were mostly Royal around that age and had a good experience with the kids clubs there? But in that area I think the lines are, mostly, more alike than not.
Some of this comes down to kid personality, but we found it helped to insist on kids club for an hour or two the first night of the cruise. This makes sure going isn’t something you put off and put off until you run out of cruise, but there are other advantages. One, a lot of kids will make friends that first night, so being there gives you better odds of your daughter having some friends she wants to see and also feeling included in activities later. Two, you get right past any initial hesitation or nervousness about the kids club and right into fun stuff, usually.
They used to (and I assume still do) publish a schedule of what activities are coming up in kids club the next day, and that helps, too. Maybe your daughter looks at the next day and isn’t wild about any of the morning activities but there’s something that evening they don’t want to miss, and that makes deciding when to go easy.
IMHO, cruising with kids is fun as long as they’re (and clearly you’re well past most or all of this) at least 3, potty trained, socially ok with going to kids club (if that age), and able to be chill for an hour of dinner or a show or whatever. If you have that it can be fun and only gets more fun as they get older and able to do more stuff, be more independent, etc.
The bad thing about it being just the two of you is that you won’t have any adult help, but the good thing is that rooms that can hold 2 people are often substantially cheaper than rooms that can hold 3 or more, especially at times when kids are out of school.
One thing to weigh in your decision of what lines or kinds of sailings you might prefer might be whether your daughter would be happier with fewer kids in the kids club and more staff attention, or the other way around. Like, we did one 14 night on Celebrity and there were like 10 kids on the entire ship that sailing – my kid was fine with that personality-wise but other kids might not be.