YOu have three options.
(1) A glyphosate based weed killer sprayed over your whole bed. You may have to repeate once or twice but most weeds should be dead by three weeks. Dig out the weeds and bin. Once glyphosate hits earth it is innactivated so once all the weeds are gone it should go along with the dead weeds BUT i'd still wait a month before letting the bunnys near it.
(2) A weed control membrane - COuld take a year to get rid of very tough weeds. Weight it down and after a few months lift it to see what is going on. Dig over and remove as many weeds as possible.
(3) Mowing.
Most weeds can't stand regular mowing so you could just turn it into a lawn. If you can afford a strimmer as a one off, strim all the weeds and bin or burn them. Give it a really good water and throw in some fast gorwing grass seed. You will probably have to water every day at the moment for about a month after planting....this will keep the grass growing fast & once grass gets going it will overtake most other weeds. Once the grass has reached about 10 cm high strim it again. Keep stimming from then on once a week. After a month switch to your normal mower and keep mowing as long at the grass grows. When the rains start in september mow mow and mow again keeping the grass as short as you possibly can. This will drain any remaining weeds of energy. Make sure you strim the edges as weeds like to grow in bits the the mower can't reach like the sides of fences.