Dinks, oversupply is where your breasts produce too much milk in effect - quite common. It's often associated with fast letdown. See this link.To be honest though her weight gain sounds spot on rather than super-fast, and as there is no greeny poo it's probably not this. However, some of what you describe does sound like it could possibly be related to having a forceful letdown. What do you think?
Some other ideas based on what you've said - it could well be reflux but here are a few other ideas:
The frequent feeding every 1-2 hours, well, probably not what what you want to hear but that sort of frequency is completely normal for a 4 week old bf baby. You can get the impression from baby books that they 'should' be going 3 hours between feeds but this is very definitely not the norm and not particularly desirable for the establishment of your milk supply in any case. Typically a baby of that age would feed at least 8-12 times in 24 hours, and often considerably more than this. Does she do any longer stints at night, sleep-wise?
Re fussing at the end of a feed - could she be full? Some babies feed extremely quickly right from the get-go, particularly if you've got an overactive letdown. My DS for example only ever fed for 5 minutes and resisted all attempts to put him back on the breast after he'd finished. Sometimes babies just want a bit of sucking time and don't necessarily want any more milk at the end of the feed. What happens if you let her suck on your little finger when she starts fussing? Alternatively, does she want to be swapped to the other side for a faster flow? - some babies get peeved when they have to work harder for their milk!
White tongue can be just milk residue, although it can also be reflux-related.
When you say that she has smelly nappies do you mean her wee smells unusual? If so I think that's something to mention to the GP perhaps. I think it's very unusal for babies this small to have wee infections but nevertheless worth checking with HV or GP. Wee in disposable nappies can have a bit of an odd smell - a bit like bovril I reckon (sorry if TMI).
Again, the catnaps could be just how your baby's wired - some just only have short sleeps unfortunately (I've had two of these babies). Or, it oculd be reflux or something else making her unsettled. It's so hard to tell but as a mum you'll have a powerful instinct as to whether something's wrong or not. Does she sleep longer if you hold her?
Gaviscon, if it's going to work, should work pretty much instantaneously. There's no need to wait two weeks for it to do something. It's not systemically absorbed, it merely works as a physical barrier to prevent the stomach contents re-emerging from the stomach.
I would second cutting out the dairy thing, it's got to be worth a try. A couple fo weeks should be enough to establish whether that's contributing to her unsettledness or not.