Unfortunately, despite your Qantas Amex being a business version you shouldn't qualify for the amex velocity platinum sign up bonus although there are reports of it coming through when signing up via a referral link. Not sure if this is still happening commonly. If you have a partner and they don't have an Amex (excepting DJ's or bank branded amex's which are exempt) then you could get them to sign up and add you for free as an accessory card holder. I'm going to be a bit cheeky and give you my referral link (100000 vleocity pts) if this is an option for you but NOTE signing up yourself may not lead to the bonus triggering due to your current Qantas amex. Good perks of 1.25pts/$ or 2.25/$ on velocity, free annual flight, 2 lounge passes to virgin lounge and 2 to amex lounge among others. $375 annual fee.
Great offer for my friends and family! - please note I get 40000 velocity points if you use my link
Alternatively as Happy mentioned the AMEX platinum charge card if you are willing to foot the annual fee ($1450) gives you the best of both worlds with flexibility to transfer to velocity, qantas (only card that currently allows this excepting Centurion), Krisflyer etc. Many other benefits too including unlimited access to VA lounges.
Good non-amex cards to combine with this
* Virgin flyer (or high flyer)- good earn and churn with a current 75000 velocity points sign up and with a $129 virgin voucher. Average ongoing earn rate of 0.66 with monthly spending caps You can often find reduced or no annual fee deals on this card. The high flyer offers a few extra benefits but is more expensive ($279) and at the moment only has 90000 velocity points sign up so not much benefit over the Flyer. Does have a better earn rate of 1pt/$.
* Coles Platinum rewards MC- earns 2 FBs/$ which when transferred to velocity equates to 0.87 velocity points/dollar + frequent transfer bonuses. Low annual fee of $89 and non international transaction fees make this a bit of a no-brainer for me although sign up bonuses are generally low.
* St George or variant Visa Amplfy Signature- Amplify or Qantas options- good sign up bonuses that often have no or reduced annual fee (usually $279)- 0.75pts/$ effectively for velocity but can also be transferred to other programs eg. KF. There is also a 10% birthday bonus on your birthday of pts earned in previous years so if you do hold it long term effectively 0.825pts/$. I churn this card though before thee year is out. Does have some other benefits including 2 priority pass lounge vouchers, insurance, concierge etc.
* Westpac Amex/MC bundle- effectively 40000 velocity pts if you take the altitude option)- 3 altitude points/1 velocity. Option of transfer to other partners as per St George. Ongoing earn rates are avg 1pt/$ on Amex and 0.4/$ on MC although intermittent transfer bonuses on top of this may be offered
There are others but I think these are the main ones. Hope this helps