AMH not a measure of egg quality though. Conception requires a genetically normal embryo, and the chances of that drop as both partners get older.
Ivf produces a larger number of embryos in one go, giving you a better chance of finding a normal embryo faster (and you only need one).
At your age I also had low amh. Not as low as yours, think it was about 3 but dropping fast, so it more than halved over 10 months and fell below the norm for my age group (also 39).
Three rounds of ivf, with Icsi all in my 39th year produced:
Round 1: 12 eggs / 8 blastocyst
Round 2: 4 eggs / 3 blastocysts
Round 3: 4 eggs / 3 blastocysts.
First round we transferred 4 embryos (1 fresh, 1 fet, 2 fet). I have low progesterone and first tow transfers I bled out before test day due to wrong progesterone dose. Round three I had an endometrial scratch and was on lubion, conceived, miscarriage at 6 weeks.
I conceived every transfer thereafter confirming to me they'd got the drugs support regime right. Two further early miscarriages.
Now 14 weeks with what looks to be a strong, healthy pregnancy I'm 40 and our ivf treatment from first stims to last transfer took almost exactly a year. Based On embryo transfer we've done since they got the drugs support right would suggest our genetically normal embryo rate is 1 in 6 blastocysts. Younger couples rate would be 1 in 2 or 1 in 3.
Though our blastocyst rate was very high, abnormally so. A friend going through treatment at a similar time would average 1 blastocysts from 4 eggs, but 1 in 2 of those balstos were normal. More blastos seems good, but as you can't tell by looking which are normal, it can just take longer to find 'the one'. If you calculate on eggs harvested to normal embryos, the hit rate for me and my friend at similar ages was similar, it's just a question of when the abnormal ones drop out.
Luck of the draw when you find that one. It wasn't 'not working' before, just a matter, for us, once the progesterone was right, of finding the embryo that will make it.
So you need to factor in whether you can afford a few rounds to find the embryo. But even with doner eggs they have to get the other things right, drug support etc. So you may need a few transfers to get that right anyway.
Maybe look for clinics that offer a three round for two deal if you want to use your own eggs?