As FyreFly said, you need to analyse *why* you hate UoM. Figure out whether it really is only institutionally specific (Don't like the structure at all, 3 hours away from home, dont offer any of the subjects you desire). Then analyse whether this will actually improve at Monash (closer to home, better structure, etc).
If it's something vague like you don't find the people very nice or something like that, there's no guarantee you'll find it subjectively better at Monash. You can only transfer into *any* degree after completing a semester.
You have two options:
(1) Stay on at Melbourne, use your melbourne uni grades as part of your selection into Monash
(2) Go on intermission and don't do any uni for a semester/year (depending when the transfer intake opens). This will only use your ATAR score.
There is little overlap between the degrees so im no]t sure if you'd be able to get any of your science subjects credited, so, you'd be essentially doing them for the heck of it. They wouldn't count towards your Monash degree (say if you were going from science at UoM to science at Monash, they obviously would count, but the degrees you are going into are fairly different).
(1) is usually the recommend option due to boredem/credit concerns. However, since it seems unlikely (contact them to be sure) that you'll get any subjects credited, there isn't as much of a point to do them if you hate it. If this is the case, perhaps go on intermission and work for awhile until you can transfer into Monash. Others may offer other opinions.
As always, triple check all these things for yourself, the repercussions can be fairly serious if we're (accidentally) wrong. Check these things with the universities to be certain (really, contact Monash ASAP for advice).