I agree with RoyalCanadian, don't lie to your child. There is nothing at all wrong with saying NO, period. She might pout a little but will get over it. If you do decide to not allow her to take it into the parks, tell her now so she will get use to the idea. Just tell her that it will be a real problem and give her some facts. No place to put her while you are on rides, too much trouble to carry, getting lost etc.
If you decide to let her take the doll, I also agree to make her carry it, no exceptions, and put it in a locker when she gets too tired. Depending on her age (over 6??) that locker money might even come out of her spending money.
It might be fun to allow her to take the doll out to dinner one night when you are not going anywhere else and the chance of getting lost is much lower.
You decide and your DD will be fine.
Jordans' mom