Can the LD1117V33 handle short peaks of up to 900mA?
No it's a pretty crap regulator and cannot be counted on to source even 800mA. The datasheet says this. 



800mA is only guaranteed with Vin-Vo = 5V and Tj = 25°C, and you have Vin-Vo = 1.7V (nominal) and hopefully you want it to work at other than 25°C. They do guarantee it will be no more than 1.3A and typically 950mA but again that's under conditions that are unrealistic. 

As I said in the comment, choose a better regulator if you have a solid spec you are trying to meet. The one you mention is probably good for 500mA with proper engineering tolerances (I didn't bother to try to figure it out). AZ1117EH-3.3TRG1 (fixed 3.3V) made by BCD in Shanghai and now available through Diodes Inc. will deliver 1A minimum and is about 0.09 USD in 1K - 7 cents if you buy a reel. A reel of 4K pcs is the same cost as 40 $7 regulators. 



Of course you may also be limited by the power dissipation but that's a whole 'nother issue. 

I do disagree with the comment from my elegantly moustachioed friend about the wisdom of dealing with Chinese suppliers for small quantity parts through eBay and Aliexpress- at least for non-hobby situations. You're better off to deal with a franchised distributor that supplies clean current date-code parts that actually are what is marked on them, unlike the cesspool of counterfeits that you may find elsewhere. For example, you can easily find 'National Semiconductor' (now gone) marked regulators with a current date code (so obviously fake) and a part number that NS (or TI) has never made. Downside is you might have higher shipping costs or a minimum order. Digikey ships to Australia for free for a fairly modest (200 AUD) order.