I do understand your reluctance to have DD upset but the longer this goes on the worse her phobia will be and it is hard to go through life being afraid of dogs...their are lots!
I agree with others talk to your friend and find a solution.
But for the future it would be so much better for D/Ds own safety to know it is not OK to scream madly when there is a dog around, at 3 she should be able to understand this.There are dogs who will react to a screaming child so for her own safety it would be sensible to address it.
I have a large calm dog who is unfazed by screetching kids, l often have several kids at my house....
There are inevitably some who are scared of him, although he is too well behaved to push, lick or jump up.....
.what l have noticed is if l speak to the nervous kids at the door and say do not scream, or yell as that is not kind to an animal,
hold my hand and just stand quietly beside me then usually after a few minutes of nothing happening child will (get bored)want to play,
then, l ensure as they come back into the kitchen where l usually am with my dog, l just repeat the message not to yell or scream and hold their hand walking through to the playroom,
honestly it has never take any child longer than a day to become much calmer and happy to walk through without panic...
However l am ALWAYS there to reassure and teach the child about my dog and dogs in general, D dog is never unattended where a child could come by and be scared...
I think if you can stop the screaming, then not pick her up everytime you pass a dog, that would be a good start.