Spiders wont really chew through plastic, unless there is a corner exposed and they can get their fangs into it, other wise their fangs will just slip off the plastic.
Tank lid plastic is fairly tough and think it will give any spider a good fangs blunting.

this size tank 450x330x330 would be a perfect size for your spider when she is an adult, and it will only cost you R120 to get the glass needed to build it!


There is a company that makes spider tanks. there is Aquahadia, he prices are good and he is normally at the expos.

Then there is Tarantula Enclosure at retail to the public

Then there is Daro, they also make tanks, but can only get the bran from pet stores.

I have a MF L.parahybana in a 60liter fishtank with the plastic lid. In the beginning she chewed the lid in a few places but once she got settled she stopped doing at.So I think your baby will be fine.