It could well be the lack of water which is causing the constipation.
When offering solids make sure LO has easy access to as much water as she wants to take, it's usually only a little tbh but she knows how much she needs. Some of her foods will contain more water than others (ie puree is usually wetter than finger food, certain fruits contain lots of water naturally, these things can help hydrate without LO taking a big drink of water) but she does need to have water offered at meals times.
Offering water with solids meals should not decrease her milk intake at all.
If you feel concerned about reduced breast feeding and prefer her to take milk rather than water then you need to offer a breast feed at/with every solids meal so she can take it as a thirst quenching drink (so it's fore milk rather than hind milk) however for practical reasons I would imagine this being after the solids rather than during her solids meal (which could be rather disruptive for you), so I'd still offer a cup of water for during the meal.
This is a great time for LO to practise using a sippy cup, put 1 or 2 oz only in the cup. This is not to limit how much she drinks it is to keep the cup light enough for her to lift and manipulate to bring up to her mouth (if she is very thirsty during a meal you can top up the cup with another oz or so). You can also help her with this during meal times and even practice a little at other times (just a few sips) by sitting her on your knee facing our, guide her hands to the cup handles and up to her mouth to show her what to do.
Banana can go either way, very ripe banana can help with constipation but unripe can make it worse.
Begin with water today, some prune or prune juice too (or the canned prune whizzed to a puree). I would suggest a trip to the doctor if she doesn't go today/tomorrow or if her stools are hard. It's better to have some temporary meds to help rather than this become a bigger problem.
