How do I know how long to wait before taking my daughter to hospital due to no bowel movement?

It is totally normal, I wouldn't force the issue anymore. As long as her poop is soft when it does come out then there is nothing wrong with it.
Breastmilk has so little waste that there isn't a whole lot to digest. FF babies poop more because there is more filler in formula.
You rally shouldn't worry about it. She will poop when she is ready.
All three of my kids did the same thing. When I started introducing cereal at 6 months they had poops more often.

Our little guy was like that. We had to use suppositories for him.

Being constipated means hard, pellet-like poops, not no poop. Like SleepingBeautee said, breastmilk has very little waste. My breastfed daughter poops only once or twice a week. She's fine. I would leave it alone & stop giving the syrup and sticking things up her behind.

Both of my children were breastfed and both went thru this....tho it was not constipation. Sometimes breastfed babies have very little waste left from the mother's milk. They use every bit of it, and that's a good thing. Please don't take her to the hospital for a non emergency issue. This only clogs ER's and makes a longer wait for people with real emergencies.

Normal for an EBF baby, as long as when she DOES go, it's not dry, hard or pellet like. I believe the record in the Breastfeeding Moms group is 20 days. My son was every 8 or 9 days. DO NOTHING as long as the stool is soft. No juice, no suppositories, no Karo (eveh their website states NOT to use it for infants, as it carries a slight risk of botulism poisioning, similar to honey in infants), especially no formula, because the iron can actually cause constipation, and upset her system as she is not used to it. Rest easy mama, this is normal, and less yucky diapers for you.  If her stool is NOT soft, and is indeed dry, hard pellets, THEN it's cause for concern.  If that is the case, let me know, and I can try to steer you in the direction of good advice.

Your baby is normal! Breastmilk has very little waste, so breastfed babies often go more than a week without a bowel movement (then there is the big explosion!).

The worst thing you can do to try to make her poop is give her formula - breastmilk is a natural laxative, formula has a tendency to constipate. One thing that helped me if my babies were "constipated" - I ate extra foods that helped ME poop, which in turn went to them through my milk. It always worked the best! Cut back on foods that constipate you and up foods that help you go - more fiber, fruits, veggies, whole grains, etc, less salt, sugar, simple carbs, etc.

if she is still eating, then she is fine. i wouldn't do any more karo syrup, juice or formula. just keep on breastfeeding. iron added to formula can constipate a baby. eat well yourself and pass on the good food she was meant to receive :)

From Is my breastfed baby constipated?

"It is also normal for a breastfed baby older than six weeks to have only one bowel movement every few days. Some healthy babies will have only one bowel movement a week. When bowel movements are less frequent, they should be more profuse in volume. As long as the baby is gaining well, wetting sufficiently, and is happy and content there is no cause to be alarmed by infrequent bowel movements, and it is not necessary to give the baby a laxative, fruit juice, or any other "helpers." In fact, attempting to force bowel movements can have harmful consequences to your baby."

Don't give her anything other than breastmilk. It's a natural laxative. Not pooping is not the same as constipation for a breastfed baby. This is completely normal, since breastmilk has little waste. Make sure the poop is soft, not hard pellets, and that's it.