Hi J.,
Your post just makes me sigh. Sometime in the last several years, tummy time has become one more thing that mothers fret over. I'm not sure why the pediatrics world has gotten their collective underpants in a bunch about this, but let me reassure you: if your kid doesn't like tummy time, it's really okay.
I've taken care of lots (lots!) of kids who all had different responses in regard to being on their stomachs as babies. Some liked it, some screamed, some fussed and hated it and some seemed ambivalent to the whole thing. They all, each and every one of them, ended up sitting, crawling and walking in their own time. My own son HATED TTime with a passion, which made sense as he had some digestive/gas issues. I don't want to lie on my stomach if it's not feeling good, so why should he? I'm not saying your daughter's stomach is bothering her, per se, just that all kids will react differently and that being in tune to what your daughter is telling you is the best you can do for her.
What will happen if your kiddo holds off on tummy time for a few months? Nothing significant. There's going to be a very broad spectrum in any group of babies in regard to when they sit up, crawl and walk. My son was on the tail end of this and while I did get a little antsy, knowing that all those other kids did it in their own time was reassurance to me.
Doctors sometimes worry about this sort of stuff, and if your kid isn't fulfilling some sort of developmental milestone by a certain date, many like to refer to pediatric occ. therapists. Only relatively recently has all this information come out about the kinds of exercise and movement our children need in order to become better walkers/eaters/etc. While it's good we have correct information (esp. in regard to toys which may cause imbalance in the muscle development and lead to incorrect walking/crawling movements), what we have to keep in mind is that billions and billions of people were just fine before the advent of Tummy Time.
Here's the big However...other than the reclined bouncy seat or carseat on travels, your daughter can certainly benefit from having opportunities to work on developing her muscles on her own. Being propped up in Bumbo-type chairs and exersaucers or Johnny Jump ups CAN be inhibiting to your child's natural movements and while these inventions may seem to soothe our children/entertain them, they can cause the muscles to develop incorrectly (esp. Exersaucer and Johnny Jump up, because they are jumping on pointed toes instead of their flat foot, which changes the leg extentions and how they use their musles. ) Better to use a few soft blankets on the floor or to hang toys on a string over baby in a moses basket or the like. Baby gyms are cute but costly and you can easily make one with string and those cheap plastic links. We had 'stations' around the house where my son could play while I worked and the string and toys just hung from doorknobs when they weren't in use.
All this to say that your daughter will likely be fine, that we receive an abundance of information (some of which can scare us and some of which is useful) and that there are other things we can do to ensure that our little ones are getting opportunities to use their bodies than just tummy time. I hope this gives you some peace of mind. She'll do it when she's ready!