House buying - Open house questions

We were thinking about checking out a few open houses today but I have a few questions.

FIRST of all, is it inappropriate to bring my five year old daughter to an open house? She is well behaved and I will not let her leave my side, but is it just tacky and annoying to bring her?

We have been preapproved, but we will likely not be putting in any offers until July after our baby has arrived and our apartment lease ends (in June). Houses are going quickly in our area and we don’t expect these to be available by the time we’re ready. Is it too soon to go look? We have been checking out homes online but we thought an open house might give us better expectations for our price range.

Thanks!