My daughter will be 3 in July.
You can use non-stimulant laxatives daily until she is past her toileting fears.
FYI, there are two basic types of laxatives: stimulant and NON-stimulant. Stimulant laxatives force bowel contractions to semi-quickly eliminate stool. They are often senna-based products (such as Senekot and Ex-lax), tho' there are others, too. The body can become dependent on stimulant laxatives, so they are for occasional use only.
NON-stimulant laxatives hold water in the stool to prevent it from getting too hard/dry. It also makes it more difficult to withhold poop (the softer the stool is, the more difficult it is to withhold poop). Non-stimulant laxatives are not habit-forming (the body does not become dependent on them), so they are safe for long-term, daily use. Some good non-stimulant laxatives are Miralax, Benefiber, Fiber Choice, Milk of Magnesia and mineral oil.
You can start by giving your dd the amount of laxative listed on the dosing guideline. You can increase or decrease the dosage, depending on how your dd responds to the laxative. If your dd gets diarrhea, then cut back on the dosage. If she can still withhold her poop on the recommended dosage, then you need to increase her dosage. You just don't want to give so much laxative that she gets chronic diarrhea and gets dehydrated, but otherwise, it is okay to give as much as is necessary for HER body. (My dd is under a doctor's care for a bowel dysmotility. At one point she was taking six laxatives a day. Another child would be very ill with that amount of laxatives, but it wasn't even quite sufficient for my dd. Each child is different and should be given what their individual body needs, rather than what an "average" child would be given.)
Some children have better success with one type of non-stimulant laxative over another, so if you get negative side effects with one, try another (for instance, some people have a hard time controlling their bowels with Miralax, so they use milk of magnesia; other people have their best success with Miralax).
You probably want to aim for poop that is pudding-like in consistency, or possibly even borderline diarrhea if dd can still withhold her poop at the pudding-like consistency.
You'll probably also want to continue the rewards for awhile every time your dd poops in the toilet. With my kids, I let them pick out the rewards, and we kept them in a box in the bathroom where they were very visible. They weren't bribes for IF they pooped but rewards for success and to lessen the trauma of pooping when it was such a scary event. My kids were very fearful for the first 1-2 weeks of daily success and moderately fearful for another 3-5 weeks after that.
sarahsmumma0710, Hi and welcome to the Toilet Teaching board.
The previous poster gave you quite a bit of wonderful advice. My suggestion would be to continue increasing your DD fiber intake with fruits and vegetables. Smoothies are a great way to increase the fiber intake. If are concerned with starting a laxative you can talk with the pediatrician and see what they recommend. I hope that helps. Please keep us updated on your DD progress.