My dtr too disliked tummy time until she was able to hold up her head really well and was more interested in moving around. I didn't push her. She was loving tummy time before I knew it. Your dtr is still very young....don't worry about it too much.
At 11 weeks she won't suffer too much from not having a lot of tummy time. Once she shows signs of holding her head up when she just on her tummy, you know she is gaining strength and will enjoy it more once she can actually turn her head and have some control over it. Like maire1210 said...putting her up on your shoulder will help develop those neck muscles. =) My son loved that so much more! A few minutes is fine if that's all she can handle for now. You don't want to stress her out with it. =) She is still so little yet and has plenty of time.
My daughter sounds a lot like Chantal's son. She didn't like tummy time until she had more control. She enjoyed it once she could roll over and really hold her head up well. Until that point, she screamed on her stomach. I used to put her up on my shoulder and that would help develop her neck muscles as well. She's perfectly healthy now with a minimal amount of tummy time as a little one. Don't worry too much. =)
She can hold her head up really well when just holding her (still a little bobbly but not much) and when I put her on her tummy on the boppy she can lift her head a little, but without the boppy she doesn't hold it up that much. I just want to make sure that by not putting her on her stomach I'm not taking away from something she should be learning to do. I do put her on her tummy daily, but its usually for just a few minutes because she fusses otherwise.
Honestly, my son never really liked tummy time. I tried to get him to do it once a day, but he just fussed, unless it was nap time (he liked to sleep on his belly, but screamed on his back) Total opposite when he would play. He loved being on his back and didn't like being on his tummy. Every baby is different and develops differently as well. My son started sitting up around 5 months and could scoot then as well. He crawled at around 7-8 months. Just because he didn't have tummy time, doesn't mean he was behind in any way. Can she hold her head up pretty well when you try? Once my son could roll over, he didn't mind being on his tummy. Try getting on the floor with her and have toys around to catch her attention and distract her a bit. And tummy time doesn't have to be a long session. Just do it as long as she isn't fussy. She'll get it soon enough!! =)