I would read it that waiting next month may be better decisions there, also possible not from that same company/peoples.
Even though your line is Child, it is weakened by the Others line, also the Parent line is clashing it from the Day and from other places...
Child line is progressing, but in this case I don't think we can read it as "all will go smoothly" as many of the other lines, including the Others are restricting, clashing or weakening it.
While waiting the Hai month may be good idea for the whole thing, these guys may not be good even then. Also there may be some other important factor missing or some important influence in making the decision may not be clear now(Resource clashing Self Line, if we view Resource as knowledge that is missing now, that seem to be against you).
Summary "How trustworthy is this carrying company for transferring my home stuffs .?"
Not much and there are other problems, so rethinking the whole think or at least the company may be wise idea. : )