My excellent pro-BF MW told us to make sure we started offering a bottle BEFORE 6 weeks if we wanted to be able to use one at all with DS.
And to offer it once a day, or every couple of days so he didn't forget.
Apparently there's a narrow window of time up to 6 weeks where babies learn how to manage a bottle teat as well as a nipple. After that they are much less able to learn, and may refuse completely.
This board has SO many women on it who took advice to wait for ages before introducing a bottle, and when their baby refused to take it, faced very worrying times going back to work etc.
We fed expressed milk from just short of 2 weeks, and it worked very well. DS is 8 months and has never had any formula.
If your DD is feeding well and gaining weight etc, I don't see why you should have problems. Clicking doesn't necessarily mean bad latch, if you have no pain and she feeds okay otherwise.
Only do it if you want to, though! Your DP might love doing a feed, but there are so many other ways he can be invaluable and be a fab dad.