Giving a date early is really difficult to do. You have your mortgage offer, searches are ordered and enquiries are being raised.
First thing, she will need the results of searches back (here they take 2-3 weeks, so areas have Councils that have been known to take 8 weeks, especially in busy times). Then she will have to look at the searches and raise any queries on them and wait for all of the replies to enquiries back.
How long replies to enquiries take is an unknown. They may arrive in in a few days, they may take weeks - my longest we waited was about 10 weeks.
When all of those are back she will report to you. At that point timescales are easy as she has control on it.
My best on dates as early as you are would be, if everything is fine on the searches and the replies come back promptly then we could be looking at end of January, but there is nothing worse than a client who then blames me if there is a problem or if they take ages to reply to enquiries and we miss the date which is why it is difficult to predict. No two transactions are the same.
By reporting to you she means an actual report on the property going through all of the information you need to know. You then sign and return paperwork if you want to go ahead. I have had people read the report and change their minds because there is something they do not like. Just because you like the house now does not mean you will when you get the report.
As you have a mortgage, she also has to comply with all of the obligations for the lender. The lender is not happy to proceed just by sending out the offer. All that means is that the valuation is okay and they would be willing to lend that much to you on that property, subject to the solicitor/conveyancer confirming the legal side is fine. There is a complete handbook of the lender's requirements that we have to check (if you are interested it is called the CML handbook and you can find the link on google). We have to check every property meets that particular lender's criteria and if there is anything which doesn't or is suspect we have to tell the lender. They then decide if they will lend. For us here, the common one is sending them the mining report, but for example if there was an access problem or a planning problem you have to refer it. If it is leasehold you may have to refer info on the rent and service charge.
It is a complicated process and takes time. It is not the best system, but it is what we have.
Phew! I went on a bit!