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Should wait until no earlier than June or July to have your credit checked for the pre-approval, so you'd have 12 months of clean credit.
IRS payment history will need to be provided, be prepared to explain the missed payment (+ all of the other lates/delinquent marks on your credit).
Don't know how much you are planning on getting approved for, or what your debt payments are, so can't say if the debt ratio would be an issue... but assuming it's not then your credit should be good enough to qualify by the end of summer.
Figure it usually takes about 30 days after your offer is accepted to close, could be a little less or more depending on how well your loan officer prepares you for the paperwork aspect and the terms of the purchase contract. How long it takes you to get your offer accepted depends on how picky you are, the inventory available, what type of sale it is (short sales & bank owned properties take longer than if you are buying a regular resale), and if you are in a competitive market or not (may have to offer on several homes before your offer is selected over another buyers).
Don't have to wait for October, while the only require for past due IRS tax debt is for it to be on a payment plan, there is no required amount of time/payments. Most lenders will require 3 months of payments, but some will just be OK with setting up and making 1 payment and then there are some which could require 12 months.