I would recommend taking a month or two to "practice" living on less discretionary income. If your rent is $2100 now and you expect a mortgage to is etimated at $3400, then pretend you're paying the full amount now (put the difference in savings). See how tight it feels to not have wiggle room for hobbies, restaurants, whatever.

If that feels okay, then do it again the following month but subtract yet another $1000 from your monthly budget to cover the unanticipated costs of first-time homeownership: repairs, maintenance, higher utilities (due to more square footage) or simply buying things like ladders and lawnmowers that renters don't need. Eventually these costs might decrease but by then your childcare costs may be a reality.

If both months feel like sustainable budgets to you, then go ahead and buy a house as planned. Otherwise, adjust your purchase price or increase your earnings or postpone your purchase.