Hello Malachi
Welcome to the forum. Is this the fin keel or wing keel version? Google them to get a lot of comment from owners.
sailboatdata.com/sailboat/catalina-250As you allude to imho this is going to be a really tough ask to sail that size yacht you potentially have just bought so far, with "inexperienced crew". Obviously I am not casting doubt on your capabilities or tenacity just wanting to respond to your post and be helpful.
There are numerous posts on this site of passages by new owners given sublime assistance by experienced sailors, to successfully make such trips from port of purchase to home port. For example this is a recent excellent one from Yeppoon to Gold Coast, and a bluepint for planning such a passage down the east coast. Obviously down the coast from the Gold Coast to Geelong throws up an absolute multitude of other hazards. Can't imagine you contemplating this trip with all on board being "quite new" to coastal passages.
www.seabreeze.com.au/forums/Sailing/General/A-Hullabaloo-along-the-Coast-I would strongly advise that you pursue more cost effective road transport methods - but the road transport operator would need to be comprehensively insured for such a trip. having said that such a more cost effective option may be hard to find.
To comment on some of your text;
1 A good survey result does not necessarily mean that the yacht is seaworthy - the surveyor can only comment on visual inspections (and hull rubber mallet tapping etc for sandwich core delaminations which I don't believe you will have the 250 is probably solid grp but check....and other such push and poke non destructive examinations............) so what happens when you get out into the Tasman Sea is what will happen depending on the conditions nothing to do with the survey report.
2 Tophat 25 footers have sailed a long way but the TH25 is a far different yacht design to the 250.........it is heavier and designed to sail offshore......and those who have sailed it a long way offshore have been very experienced and knew their yacht inside out.
Trust this is of use.