You are very confused, which is fine, and why you are here.
1. You can start practicing any time as a sole proprietor IMMEDIATELY, and bill using your social security number instead of EIN on W-9.
2. It doesn't take very long to get an EIN as a sole proprietor since you don't need to register it to the state govt.
3. Once you get an EIN, you can use it to get a corporate bank account, out of which you can pay for practice expenses, including malpractice. You now use EIN instead of your social security number on W-9s, to avoid identity theft.
4. LLC can take a while to get, depending on the state, especially if it's deemed to be a "professional LLC". But, this doesn't mean you can't get 1099 or generate practice income in the meantime. You don't wait to work before you get your LLC approved by the state government. You start working now, and once the LLC is approved, it technically ACQUIRES your sole proprietorship and take over the books if you want to do that.
You are the 100% owner of both businesses. You can acquire yourself and make yourself do stuff absorb any income in the fiscal year at anytime! Dance baby dance!!! IRS doesn't care as long as you count income and costs correctly and make no duplications or violate other rules (i.e. costs for a single business should be deducted against the income of that entity).
Of note, you can get an EIN for your LLC as soon as your LLC has a name (i.e. when the application is submitted). LLC need not be active at the state to receive income. However, lots of places want the active LLC status at the state to transact with you (i.e. banks, brokerage firms, etc.). If you want to enter into a private agreement such as to sign for a lease, it's also typically required for the entity to be active. You COULD sign contracts as an officer of LLC when it's inactive, but this has unknown and complicated implications if you later get sued by your creditors. For small practices, landlords typically want you personally to sign for the lease, so this issue is moot anyway.
My plan was: start this 1099 job in ~ 3 months and in the meantime start preparing PP. I spoke to an accountant and he told me it takes up to 12 weeks to form LLC... I can't push off 1099 job to have my LLC formed. I also was told that the entire process of PP launching can take up to 9 months due to finding office address, forming llc, getting malpractice insurance, and getting on insurance panel... i obviously cannot have 0 income for 9 months straight, so i was planning on signing with 1099 job to have a small stream of income.... if i dont have any llc/pc/sp, does that mean the 1099 income just goes straight to my personal account and if anything bad happens they can come after my house?
LLC liability protection is somewhat irrelevant for solo practices or a doctor who does 1099 since firstly the LLC carries little assets, and your creditors will sue you personally (say if you owe your landlord a bunch of rent and refuse to pay and declare LLC bankruptcy), secondly, your biggest creditor is malpractice, which is never protected by LLC. This is more relevant if you also own other assets--for example, if your practice owns commercial real estate, it's customary to create a new LLC to own that asset, so that your practice income is not subject to judgment against liens on that LLC. That said, plenty of friends/doctors own investment properties on their social security numbers. Your level of risk tolerance varies.
I'm not sure what your imagination is in that if something "bad" happens someone comes after your house. If you malpractice on 1099, your malpractice insurance pays. It's very rare to go beyond policy limits (you should read the White Coat Investor blog entry on this topic.) Are you planning on incurring risky business transactions on earning your 1099 income (i.e. work on a risky venture, owe a lot of money, and then be unable to pay back due to business negligence)? Or there are business liabilities that are not covered by personal umbrella insurance? What would they be?! These issues are very rare for an average practicing psychiatrist practicing average psychiatry. The common example I've heard is someone slip and falls on the stairs of your practice, which seems absurd on its face, but hey. Even THIS is covered now by my personal umbrella insurance since I own my own sole proprietorship. If you are really worried about these scenarios, the correct way to deal with it is to buy additional business liability coverage, not by delaying starting your business.
Why would you EVER push 1099 job starting date to when the state processes your LLC application? This makes no sense to me. These are parallel processes. You could have a 1099 job (or two) AND have 10 different side businesses that are in various stages of forming. Apply for insurance panels for ALL of these entities if you want. Who cares!?
The advantage of LLC for solo practice is mainly to make the books clean and flexible in tax planning. There are more advanced strategies for deferring taxable income (i.e. solo 401k, cash balance defined benefits plans, others). These strategies can save you HUNDREDS OF THOUSANDS on taxes each year. Some of them are available for sole proprietors, true, but the books are cleaner if you as a natural person are separate from your employer the entity. Some brokerages require a different EIN for opening certain types of accounts. You can incorporate and tax as a C-corp, which then allows you to sell portions of your practice if you want. You can treat the LLC income as an S-corp or parternship. These are options unavailable to sole proprietors.
5. There are several plausible ways to file your final year-end tax. You can use a schedule C that would deal with one entity which is the LLC that ACQUIRED your sole proprietorship and takes in all your income, or you can have multiple entities, each of which files a schedule C. Or you can file a schedule C on your own social security number. This doesn't matter (usually). Your accountant will advise you. It's typically cleaner to have one set of books for all income and costs relating to "single business activity", and it will also affect how you have contribution limits to retirement plans. But outside of that, you can do whatever you want.
Try to understand what "legal personhood" means. You are a natural person. You can form an infinite number of legal persons.