No, but mostly because of the part-time job. No money = stress. Stress isn’t good for her or the baby, and a baby should only be brought into the world when it can be financially supported, at the very least.
As for the depression, is she dependent on her meds? Does she have a history of being suicidal? Has she ever hurt herself? Is the depression under control?
“Clinical depression” isn’t necessarily a deal breaker to becoming a parent. It all depends on her mental state on and off drugs. Is she can’t go off the meds safely, then no baby should be had, for reasons above.