Well, I'm a retired chiropractor so I know a little about forces on the spine, and natural development and whatnot, and I have a serious issue with the products that allow children, who can't sit up on their own, to sit in seats like that. It's just too early in their development.
DS didn't much like being on his tummy either, and luckily, "tummy time" only needs to be for a short amount of time, and laying on mama or papa's belly, interacting and having fun, counts!
Since you're concerned about a flat head, does that mean she spends a lot of time just lying on the floor? Have you considered a sling to carry her around while you go about your daily business, or if not a "sling", a different sort of carrier (mei tai, podegi, etc)? DS absolutely thrived being up on my level, seeing what I saw, knowing what I was doing instead of just hanging out on the floor watching my ankles pass by. Of course, he enjoyed that every once in awhile, but not daily.
Also, hatred of tummy-time caused DS to turn himself over fairly quickly (we're not going to talk about how he could pull to stand at 6 months, b/c frankly that was scary and I wish he'd been slower about that).
But really, I'd figure out other ways baby could be, rather than putting her in an upright and seated position before she's really capable of doing that on her own.
And wearing babies is fun!
