If you are preparing veggies at another time of day how about making extra and saving them for her lunch the next day? I used to give mine cold veggies he wasn't bothered.
You could serve the insides of the sandwich without the toast perhaps, soup sounds good on it's own. I would make it chunky then you can drain off chunks of veg for her to eat with fingers or fork, if it's a smooth soup or broth perhaps she can try it from a cup or with a straw? Mine ate hummus with a spoon or straight into a pile of it with his hands, he wasn't bothered if there was bread or toast to go with it. Other sandwich fillers such as cheese, meat, fish or pate can be served without the bread too.
It might help to vary the type of bread, so for instance a pitta bread, tortilla wrap or chapati is less 'stodgy' than a piece of white sliced and might not be as constipating.
You could offer a prune at the same time as the toast to keep things moving - I used those soft ready to eat prunes, DS loved them, had to limit him though or he would have eaten too many!
One thing to keep in mind is that some veggies can also cause constipation, mine would get firm (or too firm) with carrots so I either served prune at the same time or on the same day. It was useful to know he got firmer with carrots and looser with prunes so really whatever else he ate I could balance out his poop with one or the other being added to his next meal.
If she is constipated and only passing small hard poos I would visit the doc. You don't want this to continue. Maybe try a day with a couple of prunes and if it doesn't resolve seek medical help, she may need some meds to help her.