I've had the problem of baby falling asleep while feeding, both ad breast and bottle fed. So you wouldn't necessarily escape it by switching to bottke.
I often do a mid-feeding diaper change. That really wakes her back up!
My kids often fell asleep nursing. My first would wake when we transitioned him to the crib - it was awful. I never gave my kids formula - just was a choice I didn't want to make. If I was making the commitment to breastfeed - i was committed and sticking with it 100% - so no bottles of formula at bed time or another time (something I am kinda proud of too). But - that being said - that was the choice I made. You need to do what works for you.
There are several things you could do to stimulate your baby while nursing if they become sleepy. Tickle feet, take off layers of clothes so they're not so warm. Talk to them...
No way dont give up that quickly! My son did the same at first but I just undressed his legs when I fed him that way you can tickle his legs and he wont be (as) warm and cosy as so less lightly to fall asleep! Also you can lightly blow on the neck or hair to rouse him is he gets sleepy!