Looks like a stars and stripes to me too. You will definitely need that upgrade, in time. These are awesome fish, very nice. However, I haven't kept one, so can't vouch for their temperament.
Check out this link, good site for species research. Sizes are generally accurate.
http://www.wetwebmedia.com/tetraodontpuffers.htm
Scientific name of stars and stripes puffer is Arothron hispidus, they get 20 inches! Scientific name of dogface puffer is Arothron nigropunctatus, they max out at 13".
One rule I have for myself - never believe information from a pet store until I verify with someone not trying to make a sale.
BTW, the going price for dogface and stars and stripes puffers is generally from about $25-50. IMO $100 was too much, and they gave you inaccurate information, causing you to buy a fish that will for sure outgrow your tank.
If you like the puffer, I'd keep it, but push them hard for at least $50 store credit. Here are some reputable online vendors - they are not the cheapest and they have a two week guarantee. Even if you add $35 shipping, the price for a medium dogface OR stars and stripes is still well under $100. And most people buy more than one fish for the flat shipping rate or split and order for someone, so actual shipping cost is usually less, and generally no sales tax.
http://www.bluezooaquatics.com/productDetail.asp?did=1&pid=328&cid=22 dogface puffer, $37-45 for small and medium
http://www.bluezooaquatics.com/productDetail.asp?did=1&pid=306&cid=22 stars and stripes puffer, $25-35 for small and medium
http://www.reefhotspot.com/store/product_info.php?cPath=21_43&products_id=732 dogface puffer, $50 for medium
http://www.reefhotspot.com/store/product_info.php?cPath=21_43&products_id=682 stars and stripes puffer, 2-4", $50
http://www.liveaquaria.com/product/prod_display.cfm?c=15+39+222&pcatid=222 common dogface puffer (Indonesia, not Solomon Islands) $35-50 for small and medium
Liveaquaria doesn't have stars and stripes in stock, but you get the idea:
1) Neither dogface nor stars and stripes puffers generally sell for $100 unless they are rare color morphs or show size
2) These are different species with different tank requirements
I'd definitely talk to the LFS about this. A lot of them take the attitude "caveat emptor". But I'd say in this economy, that would be a bad idea... They had a lot of mark-up in that fish. They should be willing to offer you store credit of at least $50 if you want to keep it. If you don't want to keep it, they should let you return it for a full refund, since it will outgrow your tank (and with this species, I think pretty quickly). A 20" fish is even big for a 300 gallon tank!
For pictures and more information on stars and stripes puffers, do a search for stars and stripes puffer for usernames Snausy and Justinreef. Here's two to get you started:
http://reefcentral.com/forums/showthread.php?t=1518027&highlight=stars+and+stripes+puffer
http://reefcentral.com/forums/showthread.php?t=1515740&highlight=stars+stripes+puffer
PS DON'T RELY ON THE LFS FOR ACCURATE INFORMATION!! If they happen to give you accurate information, great. But ALWAYS verify! I don't see how anyone knowledgeable about saltwater fish could mix up your puffer with a dogface puffer. And saying it's from Australia??? I believe stars and stripes puffers, dogface puffers and reticulated puffers are all pretty much Indo-Pacific fish (with stars and stripes having a wider range). I wouldn't call any of those Australian. I am pretty sure yours is a very nice stars and stripes puffer.