own old is she ErinMummy? Assuming she's still newborn then of course a feed will make her fall asleep, it's what feedong and having a full tummy does.
But from very tiny (like from birth) you don't have to be mega careful about not disturbing that milk-induced sleep. In fact almost the opposite, get baby used to being moved around when just falling asleep.
Yes, she'll fall asleep during a feed. I assume you wind after a feed? So when finished feeding I'd lift baby onto my shoulder to gently rub back. This may rouse slightly, but baby may well resettle on your shoulder while being winded.
Then another gentle move from shoulder, put down, swaddled, dummy in. All these will rouse slightly again, but then settle back. Then lift (swaddled and dummied) baby, little snuggle and settle to sleep.
The idea is that from day 1 you get baby used to being moved around when settling, so that you don't develop the habit that as soon as moved baby will wake.
Having said all that, this only really works if you start from a newborn