Then have some yummy treat in your pocket when she HAS to go. Or, can you put up a temporary kennel and let her loose in it to pee? Or hell, get an indoor potty pad..
It would be useful to know more about this dog. Has resource guarding been an issue in the past? Has he bitten either you or your wife before? (a real bite, not playful nipping). Or anyone else? A dog that isn't used to children may be fearful of their loudness or quick movements. Perhaps you could do some socialization work with him, e.g. hanging around places where young kids congregate to accustom him to their noise and activity. Obviously not allowing any interaction as you are unsure of his behaviour. Dogs react differently to newborns. In my experience bitches are more likely than dogs to be tolerant, but it is very much the individual dog's reaction that counts. People have been blindsided when their supposedly tolerant and gentle dog turns out to be hostile to a young child. Bottom line, no dog should be left unsupervised around young kids, so in any event you would have to monitor his behaviour carefully once your baby arrives.
On a personal note, of the five Basenjis I have owned, two bitches were entirely reliable with kids, the other was tolerant as long as they respected her space. One of the males adored children and was curious about them, the other curious but uncertain and would react to fast movements. I did not trust him and controlled any interaction closely. IMO, he would have bitten had he felt threatened. And kids, especially babies, tend to grab and pinch, ears, tails, whatever. Caution is always the safest route.
