She is lovely, I agree with the others about harlequin
Most rabbits, particularly pet shop rabbits are just mixes of lots of breeds, randomly bred.
Noones yet mentioned the actual reason not to use sawdust so here it is... the dust can cause respiritory problems (although you can get dust extracted shavings) but also because they release what are called phenols (that lovely woody smell comes from the phenols), which can also cause respiritory problems but evidence also points to them causing problems with the liver and other organs. Small animals that are kept on sawdust also seem to be more at risk when under general anesthetic. This all applies to any small animal that has its face near the shavings, although I believe rats are affected the worst. Different woods have different levels of phenols, and cedar shavings are often said to be safe because the levels of phenols in them are lower, but they are impossible to find in the UK, although you can get them in the US.
As for alternatives, I'd say megazorb would be best until she is litter trained, then just newspaper or blankets with megazorb in the litter tray. If she eats a lot of the newspaper you would want to avoid it though, some buns seem to love eating things they shouldnt! You may also want to lino the floor of the hutch, as it will stop wee soaking into the wood (which can make it stink) and also makes it easier to clean. If you cant get megazorb at the moment then carefresh is easily available at most pet shops, but it is more expensive. Megazorb is actually a horse bedding and so comes in large sacks, you can buy it at some horse/farm feed places or online. I get mine here:
https://www.thehayexperts.co.uk/Litter.11/Megazorb.174.html Of course lots of hay is good bedding too, it will keep her warm and she needs to eat a pile the size of herself every day to keep her teeth from developing painful spurs and to keep her tummy healthy. The site I linked has lots of different types of hay, so you can try her with some to see which types she likes best (they do a sample pack which is useful for this), and variety is good. Hay is the most important part of a rabbits diet and they should have it available at all times.
