Modifying for performance can certainly be done but your gains are going to be limited with that 1.6 TD lump.
The first step would be a re-map, either a decent off-the-shelf map such as that available from REVO or AMD or a custom map from a reputable tuner (don't bother with the cheap "Tuning boxes" you see on eBay, they just crudely wind up boost and fueling and the car will likely experience all kinds of issues).
Gains will depend on which variant of the 1.6 you have - it came in two power levels 88 or 110 PS, the 88PS can be mapped to ~110-114PS, the 110 to about 125-130PS with both seeing an increase in torque of about 20-25lbft.
The gains from this are not to be sniffed at - you'd certainly notice the difference. But frankly we're still talking about pretty low numbers here 130PS (your best case scenario with a map) in a car that weighs ~1,800kg isn't going to set the world alight, and it's still less than a mid-range example with the 2.0 TDI (which were 140PS, the entry level was 110PS and the GTD 170), the advantage here is bang-per-buck. £300-400 will cover a decent map. Depending on your locale you may need to inform the insurer (certainly you would in the UK) which will result in an increased premium but the difference is usually small.
As for other things you can do - You might be able to eke out another PS or two with uprated intake/air filter and exhaust but the return for the cost is going to be tiny.
Otherwise the alternative is to look to put Golfy on a diet - strip off any unneeded weight from the car, it's hard to give specific examples without knowing your particular car but things like lighter wheels, removing the spare wheel (if it has one) etc. Every kilo you remove from the car is one less kilo you need to accelerate. When it comes to acceleration performance power is only one side of the equation, weight is the other.
I will even consider changing the engine to the more powerful 2.0 TD engine but will this work?
Yeah.. just don't. Is it technically possible? Sure - it's also going to be ruinously expensive, swapping the engine on a modern car, even one that was offered as standard on the car in question is a massive undertaking. You'd have to replace all kinds of electronic and mechanical ancillaries (most likely the gearbox as well - the 2.0 uses the 6 speed 'box vs the 5 speed in the 1.6), I could go on but to be honest it's not worth it. Compared with selling it and buying a replacement that already has the 2.0 TDI it's financial suicide, and as a final in the wallet the car will likely be worth less after the conversion.
Any advice,other than selling it and buying a 2.0TD model:)
I know this isn't what you want to hear but doing this makes about a million times more sense then trying an engine swap.