Hi Marina!
Which Sydney are you in? Ontario? Down-under?
The US brands we are familar with are Tix and Stay-Brite. Neither have lead. Both have a small amount of silver. Both are primarily tin. Both are intended for jewelry. Both come with flux intended for jewelry.
In the US (and I think Canada) most tin based soft solders no longer contain lead. The label should detail the content. Check your hardware store and read the labels.
Don't use the electronics type solders that contain a rosin core. The rosin is the flux used for electronics but it does not work well for jewelry.
And if you really can't find a soft solder without lead remember that lead/tin solders were used for a long time. I remember using "30/70" solder as a kid. I fear that was probably 30% tin and 70% lead. I made it to my 60th birthday. I don't think it made me toostupid. Many stained glass artists continue to use lead "came" to build windows. It's dangerous if you breathe the fumes from molten lead or eat it or absorb it through your skin. It needs to be used with great care.
Are there other dangerous things? Yes! Many dangerous things. Breathing fumes from overheated plastic is one if you try to solder costume jewelry with plastic stones. Heating up a piece that was glued with superglue releases toxic fumes. There are way too many safety issues to try to list them here.
http://www.caseweb.com/acts/ is the website of a safety hazards group for the arts, crafts and theatre industries. You can find some guildelines there.
But if you read the labels, follow directions, and as you do, keep asking for help you should do just fine. Be careful!