As others have said, as long as you qualify for both mortgages you may get approved. Using your current home as a rental isn't a problem but using the income from that rental may not happen right away. I've understood that you need to have a signed lease and receipts of rent received. If you don't have, or can't provide that, but your income is high enough that you can afford both mortgages and other debts you may be okay. If you are reliant on the rental payments to cover your full monthly obligation you may run into trouble.
Rather than rely on our partially informed opinions, your best bet will be to sit down with a lender who can look over your full scenario and give you the best answer based on all the facts.
As a former lender as well asa current Realtor, we run these scenarios all the time and welcome the opportunity to provide you with a clear picture of your options.
I would like to recommend you visit with a mortgage planner to look at your entire situation. I can recommend a very experienced one to you.
You can certainly keep your home, rent it out, and buy a new home. You do have to establish a one year history as a landlord, to have the rental income be much of an offset against your mortgage debt.
None of us can give you a good answer because your options are a result of your total financial picture.
If you can qualify, keeping your current home as an investment property, which then creates a rental property business for you, with all the wonderful tax advantages, is a very smart strategy.
Another reason to visit with a mortgage planner is to see if the over 100% loans are available for you to lower your interest rate on your current home.